{"product_id":"9783642885099","title":"Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge","description":"\u003ch1\u003eErgebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge\u003c\/h1\u003e \u003ch2\u003eIonescu Tulcea, Alexandra; Ionescu Tulcea, C.\u003c\/h2\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2013-10-03\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783642885099\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-88507-5\u003c\/p\u003e \u003cp\u003eDimensions: 229cm x152cm\u003c\/p\u003e \u003cp\u003ePages: 192\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44481757053068,"sku":"9783642885099","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783642885099.jpg?v=1775737613","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783642885099","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}