Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica (Apr 2009)

Regulated functions and integrability

  • Ján Gunčaga

Journal volume & issue
Vol. 8, no. 1
pp. 43 – 56

Abstract

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Properties of functions defined on a bounded closed interval, weaker than continuity, have been considered by many mathematicians. Functions having both sides limits at each point are called regulated and were considered by J. Dieudonné [2], D. Fraňková [3] and others (see for example S. Banach [1], S. Saks [8]). The main class of functions we deal with consists of piece-wise constant ones. These functions play a fundamental role in the integration theory which had been developed by Igor Kluvanek (see Š. Tkacik [9]). We present an outline of this theory.