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Convergence of metric-measure spaces

2009
The central question in this chapter is the following:What does it mean to say that a metric-measure space (X, d x , vx ) is “close” to another metric-measure space (Y, d y , vy )? We would like to have an answer that is as “intrinsic” as possible, in the sense that it should depend only on the metric-measure properties of X and Y.
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On Weak Convergence of Probability Measures in a Banach Space

Journal of Mathematical Sciences, 2002
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On the Weak Convergence of Probability Measures in Orlicz Spaces

Theory of Probability & Its Applications, 1996
Necessary and sufficient conditions for weak convergence of probability measures in separable Orlicz spaces in terms of characteristic functionals and norm moments are given.
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Stochastic convergence, uniform integrability and convergence in mean on fuzzy measure spaces

Fuzzy Sets and Systems, 2002
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Inés Couso, Susana Montes, Pedro Gil
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Harmonic Functions on Metric Measure Spaces: Convergence and Compactness

Potential Analysis, 2009
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Gaczkowski, Michał, Górka, Przemysław
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On the convergence of measurable set-valued function sequence on fuzzy measure space

Fuzzy Sets and Systems, 2000
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On convergence of information in spaces with infinite invariant measure

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1968
The paper extends the ergodic theorems of information theory (Shannon-MacMillan-Breiman theorems) to spaces with an infinite invariant measure. An L1 difference theorem and a pointwisa ratio theorem are proved, for the information of spreading partitions. For the validity of the theorems it is assumed that the supremum f* of the conditional information
Klimko, E. M., Sucheston, L.
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FUZZY CONVERGENCE VERSUS WEAK CONVERGENCE IN SPACES OF PROBABILITY MEASURES

1984
If X is a separable metrizable space, then on the set \({\mathcal M}(X)\) of all probability measures on X, the structure most frequently used is the weak topology, also called topology of weak convergence. In Math. Nachr. 115, 33-57 (1984; Zbl 0593.54006), the author introduced an alternative structure, a fuzzy topology, the topological modification ...
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Convergence theorems for measures with values in Riesz spaces.

Kybernetika, 2002
Summary: In some recent papers, results of uniform additivity have been obtained for convergent sequences of measures with values in \(l\)-groups. Here a survey of these results and some of their applications are presented, together with a convergence theorem involving Lebesgue decompositions.
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