On the measurability and the Baire property of t-Wright-convex functions

Author: Olbryś, Andrzej

Source: aequationes mathematicae, Volume 68, Numbers 1-2, August 2004 , pp. 28-37(10)

Publisher: Springer

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Abstract:

J. Matkowski and M. Wróbel proved that every lower semicontinuous t-Wright-convex function is continuous. Z. Kominek proved that the continuity at a point of an arbitrary t-Wright-convex function implies its continuity everywhere. In this note we will show that every Lebesgue measurable or Baire measurable t-Wright-convex function $$ f:(a, b) \to \mathbb{R} $$ is continuous.

Keywords: 26A15; 26A51; 39B62; Convexity; Convex functions in Wright's sense

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s00010-003-2718-2

Affiliations: 1: Institute of Mathematics, Silesian University, Bankowa 14, PL-40-007, Katowice, Poland, Email: andrzej.olbrys@wp.pl

Publication date: 2004-08-01