Some properties of the normal image of convex functions

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Abstract

Let z be a convex function defined in a convex domain D of a finite-dimensional Euclidean space. Denote by z (n) the convolutions of z with elements of a d-type sequence of test functions and let ? z and ? z (n) be the measures of normal images corresponding to z and z (n). One of the main results of this work is that ? z (n)?? z in variation on a compact K ? D if and only if ? z is absolutely continuous on K with respect to Lebesgue measure. Bibliography: 9 titles.

Original languageEnglish (US)
Pages (from-to)161-171
Number of pages11
JournalMathematics of the USSR - Sbornik
Volume34
Issue number2
DOIs
StatePublished - Feb 28 1978

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