Topics in the Theory of Lifting Epub à Topics in


Topics in the Theory of Lifting [Epub] ➟ Topics in the Theory of Lifting ➤ Alexandra Ionescu Tulcea – Thomashillier.co.uk 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 19 The problem as to whether the Theory Kindle Ð 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 by von Neumann who established the existence of a lifting in this case In subseuent papers J von Neumann and M H Stone and later on Dieudonne discussed various algebraic aspects and generalizations of the problem Attemps to solve the problem as to whether Topics in Epub / 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 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 Ji' with Jia;Jib for in the Theory Epub Ú all iE eI Then she reduced the general case to this one via an isomorphism theorem concerning homogeneous measure algebras A different and direct proof of the existence of a lifting was subseuently given by the authors in ' A variant of this proof is presented in chapter .

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