On functions of bounded semivariation

TL;DR

This paper reviews the concept of bounded semivariation for Banach space-valued functions, illustrating its properties, examples, and connection to Kurzweil integration, highlighting its significance in functional analysis.

Contribution

It provides a clear summary of bounded semivariation, including examples and its relation to Kurzweil integration, enhancing understanding of this generalization of bounded variation.

Findings

Bounded semivariation extends classical variation concepts.

Examples illustrate the scope of bounded semivariation.

Connection to Kurzweil integration is outlined.

Abstract

The concept of bounded variation has been generalized in many ways. In the frame of functions taking values in Banach space, the concept of bounded semivariation is a very important generalization. The aim of this paper is to provide an accessible summary on this notion, to illustrate it with an appropriate body of examples, and to outline its connection with the integration theory due to Kurzweil.