Overview
- Authors:
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A. Ionescu Tulcea
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Northwestern University, Evanston, USA
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C. Ionescu Tulcea
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Northwestern University, Evanston, USA
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Table of contents (10 chapters)
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 1-19
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 20-33
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 34-42
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 43-53
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 54-66
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 67-85
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 86-103
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 104-132
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 133-154
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- A. Ionescu Tulcea, C. Ionescu Tulcea
Pages 155-170
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Back Matter
Pages 171-192
About this book
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.
