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In this paper we prove a representation result for essentially bounded multivalued martingales with nonempty closed convex and bounded values in a real separable Banach space. Then we turn our attention to the interplay between multimeasures and multivalued Riesz representations. Finally, we give the multivalued Radon-Nikodym property.

On natural invariant measures on generalised iterated function systems.

Käenmäki, Antti (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (2010)

Journal of the European Mathematical Society

Suppose that $μ$ is an absolutely continuous probability measure on $^{R}$ n, for large $n$ . Then $μ$ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if $n \geq {(C / ε)}^{C d}$ , then there exist $d$ -dimensional marginals of $μ$ that are $ε$ -far from being sphericallysymmetric, in an appropriate sense. Here $C > 0$ is a universal constant.

On Nikodym-type sets in high dimensions

Themis Mitsis (2004)

Studia Mathematica

We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.

On non-ergodic versions of limit theorems

Dalibor Volný (1989)

Aplikace matematiky

The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.

On nonmeasurable images

Robert Rałowski, Szymon Żeberski (2010)

Czechoslovak Mathematical Journal

Let $(X, 𝕀)$ be a Polish ideal space and let $T$ be any set. We show that under some conditions on a relation $R \subseteq T^{2} \times X$ it is possible to find a set $A \subseteq T$ such that $R (A^{2})$ is completely $𝕀$ -nonmeasurable, i.e, it is $𝕀$ -nonmeasurable in every positive Borel set. We also obtain such a set $A \subseteq T$ simultaneously for continuum many relations ${(R_{α})}_{α < 2^{ω}} .$ Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.

On nonmeasurable selectors of countable group actions

Piotr Zakrzewski (2009)

Fundamenta Mathematicae

Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.

On nonmeasurable subgroups of the real line.

Kharazishvili, A.B. (1996)

Journal of Applied Analysis

On nonparadoxical sets

Marcin Penconek (1991)

Fundamenta Mathematicae

On non-zero dimensional atoms

Reiterman, J., Rödl, V. (1979)

Abstracta. 7th Winter School on Abstract Analysis

On normal and strongly normal lattices.

Yallaoui, El-Bachir (1993)

International Journal of Mathematics and Mathematical Sciences

On normal lattices and separation and semi-separation of lattices.

Schutz, Robert W. (1992)

International Journal of Mathematics and Mathematical Sciences

On normal lattices and Wallman spaces.

Eid, George M. (1990)

International Journal of Mathematics and Mathematical Sciences

On Obtaining a Stationary Process Isomorphic to a Given Process with a Desired Distribution.

John C. Kieffer (1983)

Monatshefte für Mathematik

On one generalization of the weakly compactly generated B-spaces

Vašák, L. (1976)

Abstracta. 4th Winter School on Abstract Analysis

On Ordinary and Standard Lebesgue Measures on $ℝ^{\infty}$

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

New concepts of Lebesgue measure on $ℝ^{\infty}$ are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on $ℝ^{\infty}$ for α = (1,1,...).

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