Topology of spaces of probability measures

Банах, Тарас; Radul, Taras

doi:10.1070/sm1997v188n07abeh000241

Cited by 24 publications

(23 citation statements)

References 12 publications

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“…Then the map P * c (p D(n) ) • T : R A → P * c (X(D(n))) depends on countable many coordinates (see, for example [27]). This means that there exists a countable set D(n + 1) satisfying (5). We can assume that D(n + 1) contains D(n), which completes the induction.…”

Section: Claim 3 For Every Countable Set B ⊂ a There Exists A Countamentioning

confidence: 90%

Linear operators with compact supports, probability measures and Milyutin maps

Valov

2010

Journal of Mathematical Analysis and Applications

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The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for 0-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and κ-metrizability, are preserved under Milyutin maps.

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Section: Claim 3 For Every Countable Set B ⊂ a There Exists A Countamentioning

confidence: 90%

Linear operators with compact supports, probability measures and Milyutin maps

Valov

2010

Journal of Mathematical Analysis and Applications

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“…A possible way would be to show that K(R d ) is a G δset in M + (R d ) and then to apply the Alexandrow-Hausdorff theorem. It was shown in [4] that all probability measures from K(R d ) constitute an F σ,δ -set in M + (R d ), which still does not solve the metrization problem.…”

Section: Gamma Measuresmentioning

confidence: 99%

Gibbs states over the cone of discrete measures

Hagedorn

Kondratiev

Pasurek

et al. 2013

Journal of Functional Analysis

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We construct Gibbs perturbations of the Gamma process on R d , which may be used in applications to model systems of densely distributed particles. First we propose a definition of Gibbs measures over the cone of discrete Radon measures on R d and then analyze conditions for their existence. Our approach works also for general Lévy processes instead of Gamma measures. To this end, we need only the assumption that the first two moments of the involved Lévy intensity measures are finite. Also uniform moment estimates for the Gibbs distributions are obtained, which are essential for the construction of related diffusions. Moreover, we prove a Mecke type characterization for the Gamma measures on the cone and an FKG inequality for them.

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“…Remark. Analogous functor as in Theorem 5.5 can be built using the functor P studied by Banakh [2,3] and Banakh and Radul [5]. (For a metrizable space X, P (X) is the space of all Borel probabilistic measures supported on σ-compact subsets of X and for a map f : X → Y and µ ∈ P (X), P (f )(µ) is the transport of µ under f .)…”

Section: Note That M µ (F ) Is Continuous and Thatmentioning

confidence: 99%

Spaces of measurable functions

Niemiec

2013

Open Mathematics

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For a metrizable space X and a finite measure space (Ω M µ), the space M µ (X ) of all equivalence classes (under the relation of equality almost everywhere mod µ) of M-measurable functions from Ω to X , whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ (X ) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point. MSC:54C55, 54H05, 57N20, 54C35, 58D15

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Topology of spaces of probability measures

Cited by 24 publications

References 12 publications

Linear operators with compact supports, probability measures and Milyutin maps

Linear operators with compact supports, probability measures and Milyutin maps

Gibbs states over the cone of discrete measures

Spaces of measurable functions

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