[permalink] [id link]

Conversely, by the Riesz representation theorem, each positive linear form on arises as integration with respect to a Radon measure and is thus a continuous positive linear form on.

from
Wikipedia

## Some Related Sentences

Conversely and by

__Conversely__

**,**most realists ( specifically

**,**indirect realists ) hold that perceptions or sense data are caused

__by__mind-independent objects

**.**

__Conversely__

**,**paintings which came out of his workshop that were not necessarily physically worked

**on**

__by__Cuyp but merely overseen

__by__him technically

**,**were marked

**with**A

**.**C

**.**

**to**show that it was his instruction which saw

**the**paintings ’ completion

**.**

__Conversely__

**the**use of true brass seems

**to**have declined in Western Europe during this period in favour of gunmetals

**and**other mixed alloys but

__by__

**the**end of

**the**first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in

**the**manufacture of coins in Northumbria

**and**there

**is**archaeological

**and**historical evidence for

**the**production of brass in Germany

**and**The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout

**the**medieval period

**,**especially Dinant – brass objects are still collectively known

**as**dinanterie in French

**.**

__Conversely__

**,**if

**a**Boolean ring A

**is**given

**,**we can turn it into

**a**Boolean algebra

__by__defining x ∨ y := x + y + ( x · y )

**and**x ∧ y := x · y

**.**

__Conversely__

**,**because space

**is**expanding

**,**

**and**more distant objects are receding ever more quickly

**,**light emitted

__by__us today may never " catch up "

**to**very distant objects

**.**

__Conversely__

**,**Fleet Captain Honoré Ganteaume later reported

**the**cause

**as**an explosion

**on**

**the**quarterdeck

**,**preceded

__by__

**a**series of minor fires

**on**

**the**main deck among

**the**ship's boats

**.**

__Conversely__

**,**these arguments were disputed

__by__those who claimed Dominion was widely misunderstood

**,**

**and**conservatively inclined commenters saw

**the**change

**as**part of

**a**much larger attempt

__by__Liberals

**to**" re-brand " or re-define Canadian history

**.**

__Conversely__

**,**an absence of secure cycle-parking

**is**

**a**recurring complaint

__by__cyclists from cities

**with**low modal share of cycling

**.**

__Conversely__

**,**

**the**end of

**the**Cold War marked

__by__

**the**fall of

**the**Berlin Wall in 1989 resulted in

**a**reduction in

**the**duration of Cold War civil wars of 92 % or

**,**phrased another way

**,**

**a**roughly ten-fold increase in

**the**rate of resolution of Cold War civil wars

**.**

__Conversely__

**the**car

**is**stopped

__by__releasing pressure

**on**

**the**cable (

**with**or without completely detaching )

**and**applying

**the**brakes

**.**

__Conversely__

**,**factors that favor plate columns are: presence of solids in feed

**,**high liquid rates

**,**large column diameters

**,**complex columns

**,**columns

**with**wide feed composition variation

**,**columns

**with**

**a**chemical reaction

**,**absorption columns

**,**columns limited

__by__foundation weight tolerance

**,**low liquid rate

**,**large turn-down ratio

**and**those processes subject

**to**process surges

**.**

__Conversely__

**,**non-spontaneous electrochemical reactions can be driven forward

__by__

**the**application of

**a**current at sufficient voltage

**.**

__Conversely__

**,**badly managed food aid can create problems

__by__disrupting local markets

**,**depressing crop prices

**,**

**and**discouraging food production

**.**

__Conversely__

**,**when one wants

**to**compute an arbitrary number ( N ) of discrete samples of one cycle of

**a**

**continuous**DTFT

**,**it can be done

__by__computing

**the**relatively simple DFT of s < sub > N </ sub >,

**as**defined above

**.**

__Conversely__

**,**one might expect that inertial motions

**,**once identified

__by__observing

**the**actual motions of bodies

**and**making allowances for

**the**external forces ( such

**as**electromagnetism or friction ), can be used

**to**define

**the**geometry of space

**,**

**as**well

**as**

**a**time coordinate

**.**

__Conversely__

**,**when

**a**piece of land

**is**separated from

**the**mainland

__by__

**a**man-made canal

**,**for example

**the**Peloponnese

__by__

**the**Corinth Canal

**,**it

**is**generally not considered an island

**.**

__Conversely__

**,**people who revere or venerate religious images are (

__by__iconoclasts ) called " iconolaters ".

__Conversely__

**on**occasions he attracted criticism for dogmatically pursuing schemes favoured

__by__

**the**right of his party

**,**notably

**the**privatisation of British Rail

**,**

**and**for closing down most of

**the**coal industry in advance of privatisation

**.**

__Conversely__

**,**Trotsky held that socialism in one country would economically constrain

**the**industrial development of

**the**USSR

**,**

**and**

**thus**required assistance from

**the**new socialist countries that had arisen in

**the**developed world

**,**which was essential for maintaining Soviet democracy

**,**in 1924 much undermined

__by__civil war

**and**counter-revolution

**.**

Given

**a**field ordering ≤**as**in Def 1**,****the**elements such that x ≥ 0 forms**a****positive**cone of F**.**__Conversely__**,**given**a****positive**cone P of F**as**in Def 2**,**one can associate**a**total ordering ≤< sub > P </ sub >__by__setting x ≤ y**to**mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub > satisfies**the**properties of Def 1**.**

Conversely and representation

__Conversely__

**,**converting from an integer

__representation__

**to**

**a**floating-point one can also lose precision

**,**since

**the**floating-point type may be unable

**to**represent

**the**integer exactly ( for example

**,**might be an IEEE 754 single precision type

**,**which cannot represent

**the**integer 16777217 exactly

**,**while

**a**32-bit integer type can ).

__Conversely__

**,**if V

**is**such

**a**complex

__representation__

**,**then U can be recovered

**as**

**the**fixed point set of j (

**the**eigenspace

**with**eigenvalue 1 ).

__Conversely__

**,**pure

__representation__

**by**population creates distinct disadvantages for some Canadians

**,**giving rise

**to**frequent debate about how

**to**balance

**the**population size of electoral districts against their geographic size

**.**

__Conversely__

**,**if G contains

**a**proper non-trivial normal subgroup N

**,**then

**the**composition of

**the**natural surjective group homomorphism G → G / N

**with**

**the**regular

__representation__of G / N produces

**a**

__representation__π of G which has kernel N

**.**Taking χ

**to**be

**the**character of some non-trivial subrepresentation of π

**,**we have

**a**character satisfying

**the**hypothesis in

**the**direct statement above

**.**

__Conversely__

**,**every distributive lattice

**is**isomorphic

**to**

**a**ring of sets ; in

**the**case of finite distributive lattices

**,**this

**is**Birkhoff's

__representation__

**theorem**

**and**

**the**sets may be taken

**as**

**the**lower sets of

**a**partially ordered set

**.**

Conversely and theorem

__Conversely__

**,**for many deductive systems

**,**it

**is**possible

**to**prove

**the**completeness

__theorem__

**as**an effective consequence of

**the**compactness

__theorem__

**.**

__Conversely__

**,**

**by**

**the**inverse function

__theorem__

**,**there can be at most one value for σ that

**,**when applied

**as**an input

**to**

**,**will result in

**a**particular value for C

**.**

__Conversely__

**,**it

**is**

**a**consequence of

**the**subsequent conclusions of

**the**

__theorem__that any compact Lie group

**is**isomorphic

**to**

**a**matrix group

**.**

__Conversely__

**the**index

__theorem__for an elliptic complex can easily be reduced

**to**

**the**case of an elliptic operator:

**the**two vector bundles are given

**by**

**the**sums of

**the**even or odd terms of

**the**complex

**,**

**and**

**the**elliptic operator

**is**

**the**sum of

**the**operators of

**the**elliptic complex

**and**their adjoints

**,**restricted

**to**

**the**sum of

**the**even bundles

**.**

__Conversely__

**,**complex analytic analogues of

**the**Grothendieck – Hirzebruch – Riemann – Roch

__theorem__can be proved using

**the**families index

__theorem__

**.**

Conversely and each

__Conversely__

**,**if

**the**source of waves

**is**moving away from

**the**observer

**,**

__each__wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave

**,**so

**the**arrival time between successive waves

**is**increased

**,**reducing

**the**frequency

**.**

__Conversely__SVG

**is**an ideal PDL for print-oriented uses

**,**

**as**it contains all

**the**functionality required

**to**place

__each__glyph

**and**image in

**a**chosen location

**on**

**the**final page

**.**

__Conversely__

**,**if God

**is**incapable of being incapable

**,**then

**the**two inabilities cancel

__each__other out

**,**making God have

**the**capability

**to**do something

**.**

As stated earlier

**,**an adjunction between categories C**and**D gives rise**to****a**family of universal morphisms**,**one for__each__object in C**and**one for__each__object in D**.**__Conversely__**,**if there exists**a**universal morphism**to****a**functor G: C → D from every object of D**,**then G has**a**left adjoint**.**__Conversely__

**,**an algorithm

**to**test for solvability in arbitrary integers could be used

**to**test

**a**given equation for solvability in natural numbers

**by**applying that supposed algorithm

**to**

**the**equation obtained from

**the**given equation

**by**replacing

__each__unknown

**by**

**the**sum of

**the**squares of four new unknowns

**.**

__Conversely__

**,**any permutation

**on**corresponds

**to**

**a**cycle cover in which there

**is**an arc from vertex i

**to**vertex for

__each__i

**.**

__Conversely__

**,**

**a**thin client could download just

**the**visible parts of

**the**drawing at

**the**beginning

**and**send

__each__change back

**to**

**the**server

**to**update

**the**drawing

**.**

__Conversely__

**,**opponents have called for patience

**,**seeing

**the**mechanism employed

**by**laypeople for understanding

__each__other ’ s actions

**as**important in their formation of bases for future action when encountering similar situations

**.**

__Conversely__

**,**Y-adapter cables are available that allow two separate joysticks

**to**be connected

**to**

**a**single DA15 game adapter port ; if

**a**joystick connected

**to**one of these Y-adapters has more than two axes or buttons

**,**only

**the**first two of

__each__will work

**.**

__Conversely__

**,**he would try

**and**do something

__each__day

**to**make

**the**crowd laugh

**and**" he breathed life

**and**humour into any cricket match ".

which are linearly independent at

__each__point q in U**.**__Conversely__**,**given such**a**coframe**,**there**is****a**unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which**is**dual**to**it**,**i**.**e., satisfies**the**duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub >**is****the**Kronecker delta function**on**U**.**__Conversely__

**,**recruiting creatures which share

**a**

**positive**predisposition towards

__each__other increases their morale

**.**

__Conversely__

**,**where extra strength but

**the**smooth drive of

**a**smaller pitch

**is**required

**,**

**the**chain may be " siamesed "; instead of just two rows of plates

**on**

**the**outer sides of

**the**chain

**,**there may be three (" duplex "), four (" triplex "), or more rows of plates running parallel

**,**

**with**bushings

**and**rollers between

__each__adjacent pair

**,**

**and**

**the**same number of rows of teeth running in parallel

**on**

**the**sprockets

**to**match

**.**

*

__Conversely__**,**when**a**slow rhythm**is**heard**,**typically slower than 450 ms per beat**,**__each__beat**is**separately understood**.**__Conversely__

**,**Official Nintendo Magazines Tom East wrote that while Treecko

**is**similar

**to**Snivy due

**to**both being " green reptiles ", " they look nothing like

__each__other ".

__Conversely__

**,**

**the**AFL

**and**

**the**mill owners

**,**preferred

**to**keep negotiations between

__each__mill

**and**its own operatives

**.**

__Conversely__

**,**

**the**normed division algebras immediately give rise

**to**trialities

**by**taking

__each__V < sub > i </ sub > equal

**to**

**the**division algebra

**,**

**and**using

**the**inner product

**on**

**the**algebra

**to**dualize

**the**multiplication into

**a**trilinear

**form**

**.**

__Conversely__all Peace Mission members

**,**regardless of age

**,**race or biological relationship are viewed

**as**" Brothers "

**and**" Sisters "

**to**

__each__other under

**the**direct parentage of Father

**and**Mother Divine

**.**

__Conversely__

**,**if only one action exists for

__each__state

**and**all rewards are zero

**,**

**a**Markov decision process reduces

**to**

**a**Markov chain

**.**

__Conversely__

**,**other existentialist thinkers argue that human beings might be said

**to**actively engage

__each__other

**and**

**the**universe

**as**they communicate

**and**create

**,**

**and**loneliness

**is**merely

**the**feeling of being cut off from this process

**.**

__Conversely__

**,**

**the**southern half of its passage through Lincolnshire

**and**its northern end

**,**near Washingborough

**,**are accepted

**as**having had

**a**raised bank

**on**

__each__side ;

**the**one

**on**

**the**upland side would not be

**a**feature well adapted

**to**

**a**catchwater drain

**.**

0.235 seconds.