Abstract
On a compact space K endowed with a normalized, non negative Radon measure μ we study fields which are generated by regular closed μ-continuity sets. Especially, stability properties with respect to dense subsets and invariance results with respect to K are deduced. The Riemann- resp. Darboux integration on K is based in a natural way on these fields. We show that the Darboux integrable functions are a Banach algebra with respect to a special sup. norm. This Banach algebra has stability and invariance properties with respect to K. These properties are similar to those which characterize the uniformly continuous functions on K. A possible use of Darboux integrable functions in probability theory is explained.
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© 1984 Springer-Verlag Berlin Heidelberg
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Klein, C. (1984). Invariance Properties of the Banach Algebra of Darboux Integrable Functions. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_31
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DOI: https://doi.org/10.1007/978-3-642-45567-4_31
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