<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and generalizations of some theorems for functions with values in locally convex vector spaces replacing Banach spaces, namely Theorem: If X is a sequentially complete locally convex vector space, then the function x(・) : [a, b] → X having a bounded variation on the interval [a, b] defines a vector-valued measure m on borelian subsets of [a, b] with values in X and with the bounded variation on the borelian subsets of [a, b]; the range of this measure is also a weakly relatively compact set in X. This theorem is an extension of the results from Banach spaces to locally convex spaces.</p></abstract>

The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and generalizations of some theorems for functions with values in locally convex vector spaces replacing Banach spaces, namely Theorem: If X is a sequentially complete locally convex vector space, then the function x(・) : [a, b] → X having a bounded variation on the interval [a, b] defines a vector-valued measure m on borelian subsets of [a, b] with values in X and with the bounded variation on the borelian subsets of [a, b]; the range of this measure is also a weakly relatively compact set in X. This theorem is an extension of the results from Banach spaces to locally convex spaces.

Functions with bounded variation in locally convex space

Mathematical Institute Slovak Academy of Sciences ˇStef´anikova 49 SK–814-73 Bratislava SLOVAKIA

Université Catholique de Louvain Département de Mathématiques 2, Chemin du Cyclotron B–1348 Louvain-la-Neuve BELGIUM

Tatra Mountains Mathematical Publications

{"article-title":"Functions with bounded variation in locally convex space"}

The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and...

Functions with bounded variation in locally convex space

Publié en ligne: 13 nov. 2012

Pages: 89 - 98

DOI: https://doi.org/10.2478/v10127-011-0028-y

Mots clés
locally convex space, bounded variation, vector-valued measure on Borel subsets

This content is open access.

Functions with bounded variation in locally convex space

Publié en ligne: 13 nov. 2012

Pages: 89 - 98

DOI: https://doi.org/10.2478/v10127-011-0028-y

Mots cléslocally convex space, bounded variation, vector-valued measure on Borel subsets

This content is open access.

Mots clés
locally convex space, bounded variation, vector-valued measure on Borel subsets