Convolutions and absolute continuity
Author: D. A. Lind
Journal: Proc. Amer. Math. Soc. 39 (1973), 347-348
MSC: Primary 28A10; Secondary 43A05
MathSciNet review: 0320257
Abstract: We show that if is a subset of the circle with positive Lebesgue measure, and is integrable on almost every translate of , then is integrable on the whole circle. A generalization of this fact leads to a characterization of positive measures with nonvanishing absolutely continuous part.
Keywords: Compact group, integrable on translates, positive measure, singular measure, finiteness of convolutions, absolute continuity
Article copyright: © Copyright 1973 American Mathematical Society