A note on the Lebesgue differentiation theorem in spaces of homogeneous type. (English) Zbl 1087.28001

Toledano, R.

Real Anal. Exch. 29(2003-2004), No. 1, 335-340 (2004).

Let \(X\) be a space of homogeneous type in the sense of Coifman and Weiss. The aim of the paper is to prove that if \(X\) is a space of homogeneous type such that the balls are subspaces of homogeneous type and \(f\) is a locally integrable function then almost every point of \(X\) is a Lebesgue point of the function \(f\).

Reviewer: Leszek Skrzypczak (Poznań)

MSC:

28A15	Abstract differentiation theory, differentiation of set functions
43A85	Harmonic analysis on homogeneous spaces

Keywords:

spaces of homogeneous type; Lebesgue points