منابع مشابه
Linear liftings for non - complete probability spaces
We show that it is consistent with ZFC that L(Y,B, ν) has no linear lifting for many non-complete probability spaces (Y,B, ν), in particular for Y = [0, 1], B = Borel subsets of Y , ν = usual Radon measure on B. AMS Subject Classification 1980 (1985 revision): Primary: 28A51 Secondary: 03E35 1) Research supported by UPEI Senate Grant no 602101, by the Research Institute for Mathematical Science...
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We prove lifting results for DG modules that are akin to Auslander, Ding, and Solberg’s famous lifting results for modules. Introduction Convention. Throughout this paper, let R be a commutative noetherian ring. Hochster famously wrote that “life is really worth living” in a Cohen-Macaulay ring [7]. For instance, if R is Cohen-Macaulay and local with maximal regular sequence t, then R/(t) is ar...
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Let r; n be xed natural numbers. We prove that for n-manifolds the set of all linear natural operators T ! T T (r) is a nitely dimensional vector space over R. We construct explicitly the bases of the vector spaces. As a corollary we nd all linear natural operators T ! T r. All manifolds and maps are assumed to be innnitely diierentiable. 0. Let r; n be xed natural numbers. Given a manifold M w...
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Recent developments in formal verification have identified approximate liftings (also known as approximate couplings) as a clean, compositional abstraction for proving differential privacy. There are two styles of definitions for this construction. Earlier definitions require the existence of one or more witness distributions, while a recent definition by Sato uses universal quantification over...
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There are three important steps in the proof the BDF theorem for essentially normal operators having essential spectrum X ⊆ C. (1) Ext(X) has a neutral element. (2) Ext(X) is a group (i.e., has inverses). (3) Ext(X) depends only on the homotopy class of X. In this lecture we will exhibit the neutral element of Ext(X) and describe the generalization of that result to noncommutative C∗-algebras (...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2000
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1928