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 ∞ ( 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 ∞ ( 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 ∞

Gogi Pantsulaia (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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New concepts of Lebesgue measure on ℝ ∞ 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 ∞ for α = (1,1,...).

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 → ∫ 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 → 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 ∈ Σ } , equipped with the relative topology from L 1 ( m ) . For a subalgebra 𝒜 ⊆ Σ , let 𝒜 σ denote the generated σ -algebra and 𝒜 ¯ s denote the closure of χ ( 𝒜 ) = { χ E ; E ∈ 𝒜 } in L 1 ( m ) . Sets of the form 𝒜 ¯ s arise in criteria determining separability of L 1 ( m ) ; see [6]. We consider some natural questions concerning 𝒜 ¯ s and, in particular, its relation to χ ( 𝒜 σ ) . It is shown that...