Criteria for weak compactness of vector-valued integration maps

Susumu Okada; Werner J. Ricker

Displaying similar documents to “Criteria for weak compactness of vector-valued integration maps”

On Pettis integrals with separable range

Grzegorz Plebanek (1993)

Colloquium Mathematicae

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Several techniques have been developed to study Pettis integrability of weakly measurable functions with values in Banach spaces. As shown by M. Talagrand [Ta], it is fruitful to regard a weakly measurable mapping as a pointwise compact set of measurable functions - its Pettis integrability is then a purely measure-theoretic question of an appropriate continuity of a measure. On the other hand, properties of weakly measurable functions can be translated into the language of topological...

Representation of operators defined on the space of Bochner integrable functions.

Laurent Vanderputten (2001)

Extracta Mathematicae

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Compactness properties of vector-valued integration maps in locally convex spaces

S. Okada, S. Ricker (1994)

Colloquium Mathematicae

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Compactness properties of the integration mapassociated with a vector measure

Susumu Okada, Werner Ricker (1993)

Colloquium Mathematicae

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Topics in Weak Convergence of Probability Measures

Milan Merkle (2000)

Zbornik Radova

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Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (1995)

Annales Polonici Mathematici

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We investigate the structure of the set of solutions of the Cauchy problem x’ = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w} (I, E)$ , the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory...

Exposed points in the set of representing measures for the disc algebra

Alexander J. Izzo (1995)

Annales Polonici Mathematici

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It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.

Sequential compactness for the weak topology of vector measures in certain nuclear spaces.

Kawabe, Jun (2001)

Georgian Mathematical Journal

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On a one-dimensional analogue of the Smale horseshoe

Ryszard Rudnicki (1991)

Annales Polonici Mathematici

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We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have $\int φ (T^{n} x) f (x) d x \to \int φ d μ$ , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then $n^{- 1} \sum_{i = 0}^{n - 1} φ (T^{i} x) \to \int φ d μ$ for Lebesgue-a.e. x.