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* Theorem Every reflexive normed space is a Banach space.

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## Some Related Sentences

Theorem and Every

Theorem and normed

Theorem and space

If T

**is****a**linear operator on an arbitrary vector__space__and if there**is****a**monic polynomial P such that Af, then parts ( A ) and ( B ) of__Theorem__12 are valid for T with the proof which we gave**.**
Urysohn's

__Theorem__can be restated as: A topological__space__**is**separable and metrizable if and only if it**is**regular, Hausdorff and second-countable**.*******A

__space__elevator

**is**also constructed in the course of Clarke's final novel ( co-written with Frederik Pohl ), The Last

__Theorem__

**.**

Liouville's

__Theorem__shows that, for conserved classical systems, the local density of microstates following**a**particle path through phase__space__**is**constant as viewed by an observer moving with the ensemble ( i**.**e., the total or convective time derivative**is**zero ).
# The First Fundamental

__Theorem__of Asset Pricing: A discrete market on**a**discrete probability__space__( Ω,, )**is**arbitrage-free if and only if there exists at least one risk neutral probability measure that**is**equivalent to the original probability measure, P**.**__Theorem__( Fuglede ) Let T and N be bounded operators on

**a**complex Hilbert

__space__with N being normal

**.**

__Theorem__( Calvin Richard Putnam ) Let T, M, N be linear operators on

**a**complex Hilbert

__space__, and suppose that M and N are normal and MT

*****Green's

__Theorem__, one of several theorems that connect an integral in n-dimensional

__space__with one in ( n − 1 )- dimensional

__space__

__Theorem__: Let V be

**a**finite-dimensional vector

__space__over

**a**field F, and A

**a**square matrix over F

**.**Then V ( viewed as an F-module with the action of x given by A and extending by linearity ) satisfies the F-module isomorphism

*****T

**.**R

**.**Johansen, The Bochner-Minlos

__Theorem__for nuclear spaces and an abstract white noise

__space__, 2003

**.**

Theorem and is

In the notation of the proof of

__Theorem__12, let us take**a**look at the special case in which the minimal polynomial for T__is__**a**product of first-degree polynomials, i.e., the case in which each Af__is__of the form Af**.**__Theorem__: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there

__is__

**a**constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable

__is__computable under his definition, i**.**e**.**by one of his machines,__is__equivalent to Church's thesis by__Theorem__XXX**.**
One particularly important physical result concerning conservation laws

__is__Noether's__Theorem__, which states that there__is__**a**one-to-one correspondence between conservation laws and differentiable symmetries of physical systems**.**
:

__Theorem__( A**.**Korselt 1899 ): A positive composite integer__is__**a**Carmichael number if and only if__is__square-free, and for all prime divisors of, it__is__true that ( where means that divides ).
Even though the text

__is__otherwise inferior to the 1621 edition, Fermat's annotations — including the " Last__Theorem__"— were printed in this version**.**
Image: Thales '

__Theorem__Simple**.**svg | Thales ' theorem: if AC__is__**a**diameter, then the angle at B__is__**a**right angle**.**

Theorem and .

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of

__Theorem__10,**a**special case of this theorem__.__
Since Af are distinct prime polynomials, the polynomials Af are relatively prime (

__Theorem__8, Chapter 4 )__.__*****Lawrence C

__.__Paulson of the University of Cambridge, work on higher-order logic system, co-developer of the Isabelle

__Theorem__Prover

many small primes p, and then reconstructing B < sub > n </ sub > via the Chinese Remainder

__Theorem____.__
George Boolos ( 1989 ) built on

**a**formalized version of Berry's paradox to prove Gödel's Incompleteness__Theorem__in**a**new and much simpler way__.__
:

__Theorem__XXX: " The following classes of partial functions are coextensive, i__.__e__.__have the same members: (**a**) the partial recursive functions, ( b ) the computable functions__.__

Every and reflexive

__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__finite-dimensional

**normed**

**space**

**is**

__reflexive__, simply because in this case, the

**space**, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition

**is**bijective, by the rank-nullity theorem

**.**

__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**

**.**

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