IJPAM: Volume 40, No. 1 (2007)
AN APPROXIMATION OF THE GENERALIZED
-VARIATION IN A PERFECT SET
-VARIATION IN A PERFECT SET
Benedetto Ballarò
Department of Mathematics and Applications
University of Palermo
Via Archirafi, 34, Palermo, 90123, ITALY
e-mail: [email protected]
Department of Mathematics and Applications
University of Palermo
Via Archirafi, 34, Palermo, 90123, ITALY
e-mail: [email protected]
Abstract.We consider a function defined on a closed interval ![$[a,b]$](img2.png){kind=small}
with
values in a Banach space. We introduce the notion of generalized
-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 -variation in a perfect set
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 1
