On the lifting property (IV). Desintegration of measures

A. Ionescu-Tulcea; C. Ionescu-Tulcea

Displaying similar documents to “On the lifting property (IV). Desintegration of measures”

A note on almost strong liftings

C. Ionescu-Tulcea, R. Maher (1971)

Annales de l'institut Fourier

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Let $X$ be a locally compact space. A lifting $ρ$ of $M_{R}^{\infty} (X, μ)$ where $μ$ is a positive measure on $X$ , is almost strong if for each bounded, continuous function $f$ , $ρ (f)$ and $f$ coincide locally almost everywhere. We prove here that the set of all measures $μ$ on $X$ such that there exists an almost strong lifting of $M_{R}^{\infty} (X, | μ |)$ is a band.

On Beurling measure algebras

Ross Stokke (2022)

Commentationes Mathematicae Universitatis Carolinae

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We show how the measure theory of regular compacted-Borel measures defined on the $δ$ -ring of compacted-Borel subsets of a weighted locally compact group $(G, ω)$ provides a compatible framework for defining the corresponding Beurling measure algebra $ℳ (G, ω)$ , thus filling a gap in the literature.

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

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We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p} (μ, X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p} (μ, X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological...

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

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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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,...).

Locally $G_{δ}$ -spaces

Zdeněk Frolík (1962)

Czechoslovak Mathematical Journal

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A version of the law of large numbers

Katusi Fukuyama (2001)

Colloquium Mathematicae

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By the method of Rio [10], for a locally square integrable periodic function f, we prove $(f (μ ₁^{t} x) + . . . + f (μ ₙ^{t} x)) / n \to \int_{0}^{1} f$ for almost every x and t > 0.

Sequential closures of $σ$ -subalgebras for a vector measure

Werner J. Ricker (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a locally convex space, $m : Σ \to X$ be a vector measure defined on a $σ$ -algebra $Σ$ , and $L^{1} (m)$ be the associated (locally convex) space of $m$ -integrable functions. Let $Σ (m)$ denote ${χ_{_{E}}; E \in Σ}$ , equipped with the relative topology from $L^{1} (m)$ . For a subalgebra $𝒜 \subseteq Σ$ , let $𝒜_{σ}$ denote the generated $σ$ -algebra and ${\bar{𝒜}}_{s}$ denote the closure of $χ (𝒜) = {χ_{_{E}}; E \in 𝒜}$ in $L^{1} (m)$ . Sets of the form ${\bar{𝒜}}_{s}$ arise in criteria determining separability of $L^{1} (m)$ ; see [6]. We consider some natural questions concerning ${\bar{𝒜}}_{s}$ and, in particular, its relation to $χ (𝒜_{σ})$ . It is shown that...

Displaying similar documents to “On the lifting property (IV). Desintegration of measures”

A note on almost strong liftings

On Beurling measure algebras

Algebraic genericity of strict-order integrability

On Ordinary and Standard Lebesgue Measures on ℝ ∞

Locally G δ -spaces

A version of the law of large numbers

Sequential closures of σ -subalgebras for a vector measure

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

Locally $G_{δ}$ -spaces

Sequential closures of $σ$ -subalgebras for a vector measure