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** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

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## Some Related Sentences

** and Hahn

__**__Family † Pinheirodontidae < span style =" font-variant: small-caps ">

__Hahn__&

__Hahn__

**,**1999 </ span >

__**__Thomas Frost ( producer ), Richard King ( engineer ), Neville Marriner ( conductor ), Hilary

__Hahn__&

**the**Academy

**of**St. Martin

**in**

**the**Fields for Brahms / Stravinsky: Violin Concertos

__**__Roy Bittan

**,**Jeff Bova

**,**David Foster

**,**Humberto Gatica

**,**Jean-Jacques Goldman

**,**Rick

__Hahn__

**,**Dan Hill

**,**John Jones

**,**Aldo Nova

**,**Rick Nowels

**,**Steven Rinkoff

**,**Billy Steinberg

**,**Jim Steinman

**,**Ric Wake ( producers ) & Celine Dion for Falling Into You

__**__Thomas Frost ( producer ), Richard King ( engineer ), Sir Neville Marriner ( conductor ), Hilary

__Hahn__&

**the**Academy

**of**St. Martin

**in**

**the**Fields for Brahms: Violin Concerto / Stravinsky: Violin Concerto

__**__Todd Whitelock

**,**Tom Lazarus ( engineers ), Ken

__Hahn__( engineer / mixer ) & Jay David Saks ( engineer / mixer & producer ) for Gypsy performed by

**the**New Broadway cast with Bernadette Peters

**,**Tammy Blanchard

**,**John Dossett & others

** and –

__**__This is a distinguished work which stands out from

**,**and above

**,**many

**of**

**the**books and articles which have ben written

**in**this century on Avicenna ( Ibn Sīnā ) ( A. D. 980

__–__1037 ).

__**__

**The**numbers and are not algebraic numbers ( see

**the**Lindemann

__–__Weierstrass

**theorem**); hence they are transcendental.

__**__Haliotis brazieri f. hargravesi ( Cox

**,**1869 )

__–__synonym: Haliotis ethologus

**,**

**the**Mimic abalone

**,**Haliotis hargravesi

**,**

**the**Hargraves ’ s abalone

__**__Haliotis diversicolor squamata Reeve

**,**1846

__–__synonym: Haliotis squamata

__–__

**the**scaly Australian abalone

** and Banach

__**__

__Banach__algebra: an associative algebra A over

**the**real or complex numbers which at

**the**same time is also a

__Banach__space.

** and theorem

__**__Tarski's

__theorem__: For every infinite set A

**,**there is a bijective map between

**the**sets A and A × A.

__**__König's

__theorem__: Colloquially

**,**

**the**sum

**of**a sequence

**of**cardinals is strictly less than

**the**product

**of**a sequence

**of**larger cardinals.

__**__If S is a set

**of**sentences

**of**first-order logic and B is a consistent subset

**of**S

**,**then B is included

**in**a set that is maximal among consistent subsets

**of**S.

**The**special case where S is

**the**set

**of**all first-order sentences

**in**a given signature is weaker

**,**equivalent to

**the**Boolean prime ideal

__theorem__; see

**the**section " Weaker forms " below.

__**__

**The**Vitali

__theorem__on

**the**existence

**of**non-measurable sets which states that there is a subset

**of**

**the**real numbers that is not Lebesgue measurable.

__**__

**The**Baire category

__theorem__about complete metric spaces

**,**and its consequences

**,**such as

**the**open mapping

__theorem__and

**the**closed graph

__theorem__.

__**__Gödel's completeness

__theorem__for first-order logic: every consistent set

**of**first-order sentences has a completion.

__**__More generally

**,**Rademacher's

__theorem__extends

**the**differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set

**in**R < sup > n </ sup >, is almost everywhere differentiable.

__**__Artin reciprocity law

**,**a general

__theorem__

**in**number theory that provided a partial solution to Hilbert's ninth problem

0.237 seconds.