%0 eBook
%M Solr-EB000678827
%A Ionescu Tulcea, Alexandra
%I Springer Berlin Heidelberg
%D 1969
%C Berlin, Heidelberg
%G English
%B Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
%@ 9783642885075
%T Topics in the Theory of Lifting
%U https://doi.org/10.1007/978-3-642-88507-5?nosfx=y
%7 1st ed. 1969
%X 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 arbiĀ 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