IJPAM: Volume 40, No. 1 (2007)

AN APPROXIMATION OF THE GENERALIZED
$\mu$-VARIATION IN A PERFECT SET

Benedetto Ballarò
Department of Mathematics and Applications
University of Palermo
Via Archirafi, 34, Palermo, 90123, ITALY
e-mail: ballaro@math.unipa.it


Abstract.We consider a function defined on a closed interval $[a,b]$ with values in a Banach space. We introduce the notion of generalized $\mu$-variation in a perfect set and we establish necessary and sufficient conditions for the existence of an approximation of such variation.

Received: July 11, 2007

AMS Subject Classification: 49Q20, 26A45

Key Words and Phrases: Weierstrass-Cesari integration, functions of bounded variation, generalized $\mu$-variation in a perfect set

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1