Displaying similar documents to “In non-locally bounded L φ -spaces the norm is not almost transitive”

On the lifting property (IV). Desintegration of measures

A. Ionescu-Tulcea, C. Ionescu-Tulcea (1964)

Annales de l'institut Fourier

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Soient Z un espace localement compact μ une mesure de Radon positive sur Z et M R ∞ ( Z , μ ) l’algèbre des fonctions réelles bornées t μ -mesurables définies sur Z . Pour f ∈ M R ∞ ( Z , μ ) , g ∈ M R ∞ ( Z , μ ) on écrit f ≡ g si f et g coïncident localement presque partout. On appelle relèvement de M R ∞ ( Z , μ ) toute représentation T : f → T f de l’algèbre M R ∞ ( Z , μ ) dans l’algèbre M R ∞ ( Z , μ ) transformant 1 en 1 et telle que: T f ≡ f et T g = T h si g ≡ h . Un relèvement T : f → T f de M R ∞ ( Z , μ ) est dit fort si T f = f pour toute f ∈ C R ∞ ( Z ) . Les principaux résultats de cet article sont les théorèmes 1, 2, 3, 4. Les théorèmes...

A problem with almost everywhere equality

Piotr Niemiec (2012)

Annales Polonici Mathematici

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A topological space Y is said to have (AEEP) if the following condition is satisfied: Whenever (X,) is a measurable space and f,g: X → Y are two measurable functions, then the set Δ(f,g) = x ∈ X: f(x) = g(x) is a member of . It is shown that a metrizable space Y has (AEEP) iff the cardinality of Y is not greater than 2 ℵ ₀ .

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.

Metric transitivity and integer valued functions

Solomon Schwartzman (1960)

Annales de l'institut Fourier

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Soit X un espace mesurable de mesure μ finie ; φ : X → X une application vérifiant μ ( φ - 1 ( S ) ) = μ ( S ) pour chaque ensemble mesurable S ⊆ X . On donne des conditions nécessaires et suffisantes pour que X soit un ensemble ergodique.

Non-locally compact Polish groups and two-sided translates of open sets

Maciej Malicki (2008)

Fundamenta Mathematicae

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This paper is devoted to the following question. Suppose that a Polish group G has the property that some non-empty open subset U is covered by finitely many two-sided translates of every other non-empty open subset of G. Is then G necessarily locally compact? Polish groups which do not have the above property are called strongly non-locally compact. We characterize strongly non-locally compact Polish subgroups of S ∞ in terms of group actions, and prove that certain natural classes of...

Spaces defined by the level function and their duals

Gord Sinnamon (1994)

Studia Mathematica

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The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of L p . These domains are shown to be Banach spaces which, although closely tied to L p spaces, are not reflexive. A related construction is given which characterizes their dual spaces.