{"product_id":"topics-in-the-theory-of-lifting-von-alexandra-ionescu-tulcea-c-ionescu-tulcea","title":"Topics in the Theory of Lifting","description":"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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642885099\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642885099","offer_id":39444886552669,"sku":"9783642885099","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/cf8f79de-e25a-44c9-8d97-bf5b5fdfdee6.jpg?v=1772085589","url":"https:\/\/shop.autorenwelt.de\/products\/topics-in-the-theory-of-lifting-von-alexandra-ionescu-tulcea-c-ionescu-tulcea","provider":"Autorenwelt Shop","version":"1.0","type":"link"}