Uniqueness of measure extensions in Banach spaces

J. Rodríguez; G. Vera

Displaying similar documents to “Uniqueness of measure extensions in Banach spaces”

Descriptive properties of elements of biduals of Banach spaces

Pavel Ludvík, Jiří Spurný (2012)

Studia Mathematica

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If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball $B_{E *}$ that might possess a variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of x** are quite often determined by the behaviour of x** on the set of extreme points of $B_{E *}$ , generalizing thus results of J. Saint Raymond and F. Jellett. We also prove a result on the relation between Baire classes and intrinsic Baire...

Normal P-spaces and the $G_{δ}$ -topology

R. Levy, M. D. Rice (1981)

Colloquium Mathematicae

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A Borel extension approach to weakly compact operators on $C_{0} (T)$

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_{0} (T) = {f T \to I$ , $f$ is continuous and vanishes at infinity $}$ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$ -valued $σ$ -additive Baire measures on $T$ , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u C_{0} (T) \to X$ to be weakly compact.

The measure extension problem for vector lattices

J. D. Maitland Wright (1971)

Annales de l'institut Fourier

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Let $V$ be a boundedly $σ$ -complete vector lattice. If each $V$ -valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a $σ$ -additive measure on the generated $σ$ -field then $V$ is said to have the . Various sufficient conditions on $V$ which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: $V$ . This...

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

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For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset...

Non-separable Banach spaces with non-meager Hamel basis

Taras Banakh, Mirna Džamonja, Lorenz Halbeisen (2008)

Studia Mathematica

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We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if $| X | = κ^{ω} = 2^{κ}$ for some cardinal κ.

Complemented subalgebras of the Baire-1 functions defined on the interval $[0, 1]$ .

Shatery, H.R. (2005)

International Journal of Mathematics and Mathematical Sciences

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Typical multifractal box dimensions of measures

L. Olsen (2011)

Fundamenta Mathematicae

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We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on $ℝ^{d}$ . We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.

Some remarks on $$ -Baire-like and $b$ - $$ -Baire-like spaces

Jerzy Kąkol (1986)

Mathematica Slovaca

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On the $k$ -Baire property

Alessandro Fedeli (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this note we show the following theorem: “Let $X$ be an almost $k$ -discrete space, where $k$ is a regular cardinal. Then $X$ is $k^{+}$ -Baire iff it is a $k$ -Baire space and every point- $k$ open cover $𝒰$ of $X$ such that $card (𝒰) \leq k$ is locally- $k$ at a dense set of points.” For $k = ℵ_{0}$ we obtain a well-known characterization of Baire spaces. The case $k = ℵ_{1}$ is also discussed.