Topics in the Theory of Lifting

Topics in the Theory of Lifting The problem as to whether or not there exists a lifting of the M t 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

  • Title: Topics in the Theory of Lifting
  • Author: Alexandra Ionescu Tulcea C Ionescu Tulcea
  • ISBN: 9783642885099
  • Page: 451
  • Format: Paperback
  • 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 DieudonneThe 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 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.

    One thought on “Topics in the Theory of Lifting”

    Leave a Reply

    Your email address will not be published. Required fields are marked *