[permalink] [id link]

Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.

from
Wikipedia

## Some Related Sentences

Every and random

__Every__physical system, however, when microscopically examined, shows apparently

__random__microscopic statistical fluctuations in its thermodynamic variables of state ( entropy, temperature, pressure, etc .).

__Every__two months these bags were taken from

**the**church of Santa Croce, where they were ordinarily kept, and in

**a**short ceremony drawn out at

__random__

**.**

__Every__club in

**the**league competes in this knockout tournament

**with**2 teams being given

**a**

__random__bye

**to**

**the**2nd Round

**.**

__Every__year

**the**Lions host

**the**Harvey Martin Classic at

**the**Cotton Bowl in Dallas and play host

**to**

**a**

__random__LSC opponent

**to**reach out

**to**

**the**numerous Dallas alumni and also most of

**the**Lion football players are from

**the**DFW area

**.**

__Every__3 helis destroyed would give players

**a**weapon or an extra ( see below ) or if

**the**player had destroyed

**the**heli from above ( using

**a**hyperjump )

**a**

__random__weapon smaller in quantity was gained

**.**

Every and vector

__Every__subset A of

**the**

__vector__space is contained within

**a**smallest convex set ( called

**the**convex hull of A ), namely

**the**intersection of all convex sets containing A

**.**

__Every__

__vector__v in determines

**a**linear map from

**R**

**to**taking 1

**to**v, which can be thought of

**as**

**a**Lie

**algebra**homomorphism

**.**

__Every__

__vector__space has

**a**basis, and all bases of

**a**

__vector__space have

**the**same number of elements, called

**the**dimension of

**the**

__vector__space

**.**

__Every__normed

__vector__space V sits

**as**

**a**dense subspace inside

**a**Banach space ; this Banach space is essentially uniquely defined by V and is called

**the**completion of V

**.**

__Every__finite-dimensional

__vector__space is isomorphic

**to**its dual space, but this isomorphism relies

**on**an arbitrary choice of isomorphism ( for example, via choosing

**a**basis and then taking

**the**isomorphism sending this basis

**to**

**the**corresponding dual basis ).

__Every__continuous function in

**the**function space can be represented

**as**

**a**linear combination of basis functions, just

**as**every

__vector__in

**a**

__vector__space can be represented

**as**

**a**linear combination of basis vectors

**.**

__Every__finite-dimensional Hausdorff topological

__vector__space is reflexive, because J is bijective by linear

**algebra**, and because there is

**a**unique Hausdorff

__vector__space topology

**on**

**a**finite dimensional

__vector__space

**.**

__Every__coalgebra, by (

__vector__space ) duality,

**gives**

**rise**

**to**an

**algebra**, but not in general

**the**other way

**.**

*

__Every__holomorphic__vector__bundle**on****a**projective variety is induced by**a**unique algebraic__vector__bundle**.**
For example, second-order arithmetic can express

**the**principle "__Every__countable__vector__space has**a**basis " but it cannot express**the**principle "__Every____vector__space has**a**basis ".
Many principles that imply

**the**axiom of choice in their general form ( such**as**"__Every____vector__space has**a**basis ") become provable in weak subsystems of second-order arithmetic when they are restricted**.**__Every__

__vector__space is free, and

**the**free

__vector__space

**on**

**a**set is

**a**special case of

**a**free module

**on**

**a**set

**.**

Every and gives

__Every__Boolean

**algebra**( A, ∧, ∨)

__gives__

**rise**

**to**

**a**ring ( A, +, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation is called symmetric difference in

**the**case of sets and XOR in

**the**case of logic ) and

**a**· b :=

**a**∧ b

**.**The zero element of this ring coincides

**with**

**the**0 of

**the**Boolean

**algebra**;

**the**multiplicative identity element of

**the**ring is

**the**1 of

**the**Boolean

**algebra**

**.**

__Every__LORAN chain in

**the**world uses

**a**unique Group Repetition Interval,

**the**number of which, when multiplied by ten,

__gives__how many microseconds pass between pulses from

**a**given station in

**the**chain

**.**

__Every__year,

**the**International Documentary Festival in Amsterdam ( IDFA )

__gives__an acclaimed filmmaker

**the**chance

**to**screen his or her personal Top 10 favorite films

**.**

*

__Every__finite topological space__gives__**rise****to****a**preorder**on**its points, in which x ≤ y if and only if x belongs**to**every neighborhood of y, and every finite preorder can be formed**as****the**specialization preorder of**a**topological space in this way**.**__Every__thing depends upon

**the**evil of

**the**second order ; it is this which

__gives__

**to**such actions

**the**character of crime, and which makes punishment necessary

**.**

__Every__adjunction 〈 F, G, ε, η 〉

__gives__

**rise**

**to**an associated monad 〈 T, η, μ 〉 in

**the**category D

**.**The functor

__Every__ticket is provided

**with**

**a**bar code that

__gives__information about

**the**time

**the**visitor stepped into

**the**museum

**.**

__Every__broadcasting company has members and

**the**number of members

__gives__them

**a**status that is connected

**to**

**the**number of hours of broadcasting

**.**

The WBC launched

**a**website called Priests Rape Boys in which they criticize**the**Roman Catholic Church because of**the**Catholic sex abuse scandal, saying, "__Every__time any person__gives__any amount of money**to****the**Catholic Church, that person is paying**the**salary of pedophile rapists**.**__Every__year,

**the**magazine

__gives__out its Utne Independent Press Awards, which honor alternative and independent magazines from around

**the**world

**.**

This flat may be identified

**with****the**partition of**the**vertices of into**the**connected components of**the**subgraph formed by:__Every__set of edges having**the**same closure**as**__gives__**rise****to****the**same partition of**the**vertices, and may be recovered from**the**partition of**the**vertices,**as**it consists of**the**edges whose endpoints both belong**to****the**same set in**the**partition**.**__Every__sequence of A, B, and C without immediate repetition of

**the**same one is possible and

__gives__an equally dense packing for spheres of

**a**given radius

**.**

__Every__year

**the**American Society of Architectural Illustrators

__gives__out

**the**Hugh Ferriss Memorial Prize for architectural rendering excellence

**.**

__Every__year,

**the**IDFA, International Documentary Festival in Amsterdam,

__gives__an acclaimed filmmaker

**the**chance

**to**screen his or her personal Top 10 favorite films

**.**

__Every__year, she

__gives__

**a**speech

**to**cadets from throughout Civil Air Patrol at

**the**National Honor Guard Academy and also

**to**

**a**gathered assembly of basic cadets and staff at

**the**Civil Air Patrol's Tri-Wing Encampment, held by Maryland Wing

**.**

__Every__episode

__gives__credits

**to**James Burrows, Glen Charles and Les Charles,

**the**creators of Cheers,

**the**show where

**the**character of Dr

**.**Frasier Crane originated

**.**

0.500 seconds.