Topics in the Theory of Lifting - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge - Alexandra Ionescu Tulcea - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783642885099 - October 3, 2013
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Alexandra Ionescu Tulcea
Topics in the Theory of Lifting - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge Softcover Reprint of the Original 1st Ed. 1969 edition

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The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 [102] by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone [105], and later on 1. Dieudonne [22], discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 [88], D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi­ trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras [87], [88]. A different and more direct proof of the existence of a lifting was subsequently given by the authors in [65]' A variant of this proof is presented in chapter 4.

192 pages, 1 black & white illustrations, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released October 3, 2013
ISBN13 9783642885099
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 192
Dimensions 152 × 229 × 11 mm   ·   281 g
Language English  

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