EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Vol. CXXII, No. 26, pp. 133–144 (2001)

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A new quantitative analysis of some basic principles of the theory of functions of a real variable

S. Todorcevic

Institute of Mathematics, SANU, Knez Mihailova 15, 11000 Beograd, Yugoslavia

Abstract: We define and study a new regularity requirement that one can put on sets of reals where a given function is to be continuous. The requirement is expressed in terms of number systems used in representing reals as strings of digits. We compare it with the classical requirement expressed in terms of the Lebesgue measure.

Keywords: measurable, continuous

Classification (MSC2000): 28A05, 28A10, 26A21, 05D10

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Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 20 Jun 2011.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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