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A new quantitative analysis of some basic principles of the theory of functions of a real variable. (English) Zbl 1005.28001

Summary: The author defines and studies 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. He compares it with the classical requirement expressed in terms of the Lebesgue measure.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
26A21 Classification of real functions; Baire classification of sets and functions
28A10 Real- or complex-valued set functions
28A12 Contents, measures, outer measures, capacities
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