Article contents
Refinement-Unbounded Interval Functions and Absolute Continuity
Published online by Cambridge University Press: 20 November 2018
Extract
In this paper we prove the following characterization theorem (Section 3) :
Theorem 1. If each of g and m is a real-valued non-decreasing function on the number interval [a, b], then the following two statements are equivalent: (1) If R is a real-valued, refinement-unbounded (Section 3) function of subintervals of [a, b], then the integral (Section 2)
exists and is equal to g (b) — g (a), and
(2) g is absolutely continuous with respect to m.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1965
References
- 2
- Cited by