<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 spaces, especially functions having weakly compact semivariation and generalizations of some theorems for functions with values in locally convex vector spaces, namely: If <italic>X </italic>is a sequentially complete locally convex vector space, then the function <italic>x</italic>(⋅): [<italic>a, b</italic>] →<italic> X </italic>having a weakly compact semivariation on the interval [<italic>a, b</italic>] defines a vector valued measure <italic>m</italic> on Borel subsets of [<italic>a, b</italic>] with values in <italic>X </italic>and the range of this measure is a weakly relatively compact subset in <italic>X</italic>. This theorem is an extension of the result of Sirvint and of Edwards 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 spaces, especially functions having weakly compact semivariation and generalizations of some theorems for functions with values in locally convex vector spaces, namely: If X is a sequentially complete locally convex vector space, then the function x(⋅): [a, b] → X having a weakly compact semivariation on the interval [a, b] defines a vector valued measure m on Borel subsets of [a, b] with values in X and the range of this measure is a weakly relatively compact subset in X. This theorem is an extension of the result of Sirvint and of Edwards from Banach spaces to locally convex spaces.

Functions with values in locally convex spaces with weakly compact semivariation

Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814-73 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Functions with values in locally convex spaces with weakly compact semivariation"}

The present paper is concerned with some properties of functions with values in locally convex vector spaces, especially functions having weakly compact...

Functions with values in locally convex spaces with weakly compact semivariation

Published Online: Nov 19, 2012

Page range: 133 - 139

DOI: https://doi.org/10.2478/v10127-012-0033-9

Keywords
locally convex space, weakly compact semivariation, vector valued measure on Borel subsets.

This content is open access.

Functions with values in locally convex spaces with weakly compact semivariation

Published Online: Nov 19, 2012

Page range: 133 - 139

DOI: https://doi.org/10.2478/v10127-012-0033-9

Keywordslocally convex space, weakly compact semivariation, vector valued measure on Borel subsets.

This content is open access.

Keywords
locally convex space, weakly compact semivariation, vector valued measure on Borel subsets.