منابع مشابه
The Lebesgue Monotone Convergence Theorem
For simplicity, we adopt the following rules: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, E is an element of S, F , G are sequences of partial functions from X into R, I is a sequence of extended reals, f , g are partial functions from X to R, s1, s2, s3 are sequences of extended reals, p is an extended real number, n, m are natural numbers, x is an element of X...
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Scientiic codes which use iterative methods are often diicult to parallelize well. Such codes usually contain while loops which iterate until they converge upon the solution. Problems arise since the number of iterations cannot be determined at compile time, and tests for termination usually require a global reduction and an associated barrier. We present a method which allows us avoid performi...
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The monotone convergence theorem holds for the Riemann integral, provided (of course) it is assumed that the limit function is Riemann integrable. It might be thought, though, that this would be difficult to prove and inappropriate for an undergraduate course. In fact the identity is elementary: in the Lebesgue theory it is only the integrability of the limit function that is deep. This article...
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We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch–Brezis type.
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This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finitedimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of con...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2006
ISSN: 0021-9002,1475-6072
DOI: 10.1239/jap/1158784934