On a question of E.A. Michael

Vladimir V. Filippov

Displaying similar documents to “On a question of E.A. Michael”

Continuous version of the Choquet integral representation theorem

Piotr Puchała (2005)

Studia Mathematica

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Let E be a locally convex topological Hausdorff space, K a nonempty compact convex subset of E, μ a regular Borel probability measure on E and γ > 0. We say that the measure μ γ-represents a point x ∈ K if $s u p_{| | f | | \leq 1} | f (x) - \int_{K} f d μ | < γ$ for any f ∈ E*. In this paper a continuous version of the Choquet theorem is proved, namely, if P is a continuous multivalued mapping from a metric space T into the space of nonempty, bounded convex subsets of a Banach space X, then there exists a weak* continuous family $(μ_{t})$ of...

Morse-Sard theorem for delta-convex curves

D. Pavlica (2008)

Mathematica Bohemica

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Let $f : I \to X$ be a delta-convex mapping, where $I \subset ℝ$ is an open interval and $X$ a Banach space. Let $C_{f}$ be the set of critical points of $f$ . We prove that $f (C_{f})$ has zero $1 / 2$ -dimensional Hausdorff measure.

Lineability and spaceability on vector-measure spaces

Giuseppina Barbieri, Francisco J. García-Pacheco, Daniele Puglisi (2013)

Studia Mathematica

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It is proved that if X is infinite-dimensional, then there exists an infinite-dimensional space of X-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that $c a (ℬ, λ, X) ∖ M_{σ}$ , the measures with non-σ-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear...

A generalization of the Schauder fixed point theorem via multivalued contractions

Paolo Cubiotti, Beatrice Di Bella (2001)

Commentationes Mathematicae Universitatis Carolinae

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We establish a fixed point theorem for a continuous function $f : X \to E$ , where $E$ is a Banach space and $X \subseteq E$ . Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.