Regulated functions and integrability
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Źródło: Annales Universitatis Paedagogicae Cracoviensis. 70, Studia Mathematica 8 (2009), s. [43]-56
Język: en
Data: 2009
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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 constamt 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.