Displaying similar documents to “Radon-Nikodym property for vector-valued integrable functions”

On vector valued measure spaces of bounded Φ -variation containing copies of ℓ ∞

María J. Rivera (2001)

Czechoslovak Mathematical Journal

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Given a Young function Φ , we study the existence of copies of c 0 and ℓ ∞ in c a b v Φ ( μ , X ) and in c a b s v Φ ( μ , X ) , the countably additive, μ -continuous, and X -valued measure spaces of bounded Φ -variation and bounded Φ -semivariation, respectively.

On Vitali-Hahn-Saks-Nikodym type theorems

Barbara T. Faires (1976)

Annales de l'institut Fourier

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A Boolean algebra 𝒜 has the interpolation property (property (I)) if given sequences ( a n ) , ( b m ) in 𝒜 with a n ≤ b m for all n , m , there exists an element b in 𝒜 such that a n ≤ b ≤ b n for all n . Let 𝒜 denote an algebra with the property (I). It is shown that if ( μ n : 𝒜 → X ) ( X a Banach space) is a sequence of strongly additive measures such that lim n μ n ( a ) exists for each a ∈ 𝒜 , then μ ( a ) = lim n μ n ( a ) defines a strongly additive map from 𝒜 to X the μ n ' s are uniformly strongly additive. The Vitali-Hahn-Saks (VHS) theorem for strongly additive...

On some ergodic properties for continuous and affine functions

Charles J. K. Batty (1978)

Annales de l'institut Fourier

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Two problems posed by Choquet and Foias are solved: (i) Let T be a positive linear operator on the space C ( X ) of continuous real-valued functions on a compact Hausdorff space X . It is shown that if n - 1 ∑ r = 0 n - 1 T r 1 converges pointwise to a continuous limit, then the convergence is uniform on X . (ii) An example is given of a Choquet simplex K and a positive linear operator T on the space A ( K ) of continuous affine real-valued functions on K , such that inf { ( T n 1 ) ( x ) : n ≥ } < 1 for each...

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.

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...