This article is cited in 1 paper

Approximate symmetric variation and the Lusin $N$-property

V. A. Skvortsov

M. V. Lomonosov Moscow State University

Abstract: An example is constructed of a continuous function having an approximate symmetric derivative everywhere, yet not having the Lusin $N$-property. The same example proves the existence of a continuous function whose approximate variation on some set of measure zero is non-zero, but whose approximate symmetric variation on the same set is zero.

MSC: Primary 26A24, 26A45; Secondary 28A15, 26A30, 26A39

Received: 25.09.1995

DOI: 10.4213/im140

 English version: Izvestiya: Mathematics, 1997, 61:4, 831–841

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