scholarly journals THOMSON'S VARIATIONAL MEASURE AND NONABSOLUTELY CONVERGENT INTEGRALS

2000 ◽  
Vol 26 (1) ◽  
pp. 35 ◽  
Author(s):  
Ene
Keyword(s):  
Variational Measure

A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Valentin Skvortsov ◽  
Francesco Tulone
Keyword(s):  
Measure Space ◽  
Henstock Integral ◽  
Type Integral ◽  
Topological Measure ◽  
Variational Measure

Abstract We introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil–Henstock-type integral related to this basis. We prove a version of Hake’s theorem in terms of a variational measure.

scholarly journals McShane Integrability Using Variational Measure

2020 ◽  
Vol 13 (2) ◽  
pp. 303-313
Author(s):  
Felipe Raypan Sumalpong Jr ◽  
Julius V. Benitez
Keyword(s):  
Measurable Subset ◽  
Variational Measure

If f : [a, b] → R is McShane integrable on [a, b], then f is McShane integrable on every Lebesgue measurable subset of [a, b]. However, integrability of a real-valued function on [a, b] does not imply McShane integrability on any E ⊆ [a, b]. In this paper, we give a characterization for the McShane integrability of f : [a, b] → R over E ⊆ [a, b] using concept of variational measure.

scholarly journals On the $\sigma $-finiteness of a variational measure

2003 ◽  
Vol 128 (2) ◽  
pp. 137-146
Author(s):  
Diana Caponetti
Keyword(s):  
Variational Measure

Variational measures and the Kurzweil-Henstock integral

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Štefan Schwabik
Keyword(s):  
Continuous Function ◽  
Total Variation ◽  
Integrable Function ◽  
Interval Function ◽  
Total Change ◽  
Henstock Integral ◽  
Additive Interval Function ◽  
Variational Measure ◽  
Indefinite Integral ◽  
Interval Functions

AbstractFor a given continuous function F on a compact interval E in the set ℝ of reals the problem is how to describe the “total change” of F on a set M ⊂ E. Full variational measures W F(M) and V F(M) (see Section 2) in the sense presented by B. S. Thomson are introduced in this work to this aim. They are generated by two slightly different interval functions, namely the oscillation of F over an interval and the value of the additive interval function generated by F, respectively. They coincide with the concept of classical total variation if M is an interval and they are zero if on the set M the function F is of negligible variation.The Kurzweil-Henstock integration is shortly described and some of its properties are studied using the variational measure W F(M) for the indefinite integral F of an integrable function f.

scholarly journals THOMSON'S VARIATIONAL MEASURE

1998 ◽  
Vol 24 (2) ◽  
pp. 523 ◽  
Author(s):  
Ene
Keyword(s):  
Variational Measure
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