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