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* Every set of reals in L ( R ) is Lebesgue measurable ( in fact, universally measurable ) and has the property of Baire and the perfect set property.

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## Some Related Sentences

Every and set

__Every__such subset

**has**a smallest element

**,**so to specify our choice function we can simply say that it maps each

__set__to

**the**least element

**of**that

__set__

**.**

** Zorn's lemma:

__Every__non-empty partially ordered__set__**in**which every chain**(**i**.**e**.**totally ordered subset**)****has**an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered__set__**has**a maximal totally ordered subset "**is**also equivalent to AC over ZF**.*******

__Every__continuous functor on a small-complete category which satisfies

**the**appropriate solution

__set__condition

**has**a left-adjoint

**(**

**the**Freyd adjoint functor theorem ).

*****

__Every__continuous map from a compact space to a Hausdorff space

**is**closed

**and**proper

**(**i

**.**e.,

**the**pre-image

**of**a compact

__set__

**is**compact

**.**

__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__corporation

**,**whether financial or union

**,**as well as every division

**of**

**the**administration

**,**were

__set__up as branches

**of**

**the**party

**,**

**the**CEOs

**,**Union leaders

**,**

**and**division directors being sworn-in as section presidents

**of**

**the**party

**.**

__Every__DNS zone must be assigned a

__set__

**of**authoritative name servers that are installed

**in**NS records

**in**

**the**parent zone

**,**

**and**should be installed

**(**to be authoritative records

**)**as self-referential NS records on

**the**authoritative name servers

**.**

Group actions / representations:

__Every__group G can be considered as a category with a single object whose morphisms are**the**elements**of**G**.**A functor from G to Set**is**then nothing but a group action**of**G on a particular__set__**,**i**.**e**.**a G-set**.**
# " Personality " Argument: this argument

**is**based on a quote from Hegel: "__Every__man**has****the**right to turn his will upon a thing or make**the**thing an object**of**his will**,**that**is**to say**,**to__set__aside**the**mere thing**and**recreate it as his own ".__Every__atom across this plane

**has**an individual

__set__

**of**emission cones .</ p > < p > Drawing

**the**billions

**of**overlapping cones

**is**impossible

**,**so this

**is**a simplified diagram showing

**the**extents

**of**all

**the**emission cones combined

**.**

*****

__Every__preorder can be given a topology

**,**

**the**Alexandrov topology ;

**and**indeed

**,**every preorder on a

__set__

**is**

**in**one-to-one correspondence with an Alexandrov topology on that

__set__

**.**

__Every__binary relation

**R**on a

__set__S can be extended to a preorder on S by taking

**the**transitive closure

**and**reflexive closure

**,**

**R**< sup >+=</ sup >.

Every and reals

*****

__Every__real Banach algebra which

**is**a division algebra

**is**isomorphic to

**the**

__reals__

**,**

**the**complexes

**,**or

**the**quaternions

**.**

*****

__Every__unital real Banach algebra with no zero divisors

**,**

**and**

**in**which every principal ideal

**is**closed

**,**

**is**isomorphic to

**the**

__reals__

**,**

**the**complexes

**,**or

**the**quaternions

**.**

*****

__Every__projective

**set**

**of**

__reals__--

**and**therefore every analytic

**set**

**and**every Borel

**set**

**of**

__reals__--

**is**an element

**of**

**L**

**(**

**R**).

Every and L

__Every__car uses either a 5

**.**0

__L__Ford " Boss 302 " SVO or a 5

**.**0

__L__Chevrolet small block race-engine

**(**depending on

**the**make )-capable

**of**producing between 460

**and**485 kW

**(**620 — 650 bhp

**)**

**of**power

**,**but generally quoted as a little over 450 kW

**(**600 bhp

**)**

**in**race trim

**.**

__Every__square-integrable vector field u ∈

**(**

__L__< sup > 2 </ sup >( Ω ))< sup > 3 </ sup >

**has**an orthogonal decomposition:

__Every__musician

**in**

__L__

**.**A

**.**wanted to participate

**,**but soon Lennon's drinking

**and**Spector's erratic behavior

**(**which included his firing a gun

**in**

**the**studio control room

**)**caused

**the**sessions to break down

**.**

*****Let K < sup > a </ sup > be an algebraic closure

**of**K containing

__L__

**.**

__Every__embedding σ

**of**

__L__

**in**K < sup > a </ sup > which restricts to

**the**identity on K

**,**satisfies σ

**(**

__L__

**)**=

__L__

**.**In other words

**,**σ

**is**an automorphism

**of**

__L__over K

**.**

__Every__non-trivial problem

**in**

__L__

**is**complete under log-space reductions so weaker reductions are required to identify meaningful notions

**of**L-completeness

**,**

**the**most common being first-order reductions

**.**

Russell

__L__**.**Ackoff wrote about complex problems as messes: "__Every__problem interacts with other problems**and****is**therefore part**of**a**set****of**interrelated problems**,**a system**of**problems ….
Professor Herman Bondi

**,**who gave**the**first J**.**__L__**.**Synge Public Lecture**in**1992**,**had this to say: "__Every__one**of****the**other 88 %**has**been deeply influenced by his geometric vision**and****the**clarity**of**his expression ".__Every__

__L__

**.**A

**.**# 1 song would be played

**in**chronological order

**(**utilizing

**the**older KHJ radio charts

**and**other local charts

**)**from 1955 through 1985

**.**

__Every__commutative von Neumann algebra on a separable Hilbert space

**is**isomorphic to

__L__< sup >∞</ sup >( X

**)**for some standard measure space

**(**X

**,**μ

**)**

**and**conversely

**,**for every standard measure space X

**,**

__L__< sup >∞</ sup >( X

**)**

**is**a von Neumann algebra

**.**

__Every__Data Matrix

**is**composed

**of**two solid adjacent borders

**in**an "

__L__" shape

**(**called

**the**" finder pattern ")

**and**two other borders consisting

**of**alternating dark

**and**light " cells " or modules

**(**called

**the**" timing pattern ").

__Every__year since 1994

**,**Lloydies have climbed onto

**the**top

**of**Millikan Library to construct

**the**Lloyd Christmas Tree

**,**a monumental structure

**of**numerous Christmas lights strung together to resemble a 10-story Christmas tree topped with a 12-feet-tall "

__L__." The latest off-campus pranks have been

**the**pranking

**of**MIT's Campus Preview Weekend

**,**which included many Lloydies

**.**

*****James Allen ’ s Book

**of**Meditations for

__Every__Day

**in**

**the**Year

**(**1913

**)**

**of**earlier texts

**,**compiled by his wife Lily

__L__

**.**Allen

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