Continuous singular measures with absolutely continuous convolution squares on locally compact groups (Q805980)

The existence of singular measures on abelian groups with absolutely continuous convolution squares is well known [\textit{E. Hewitt} and \textit{H. Zuckerman}, Proc. Camb. Philos. Soc. 62, 399-420 (1966; Zbl 0148.381)]. In the paper under review the authors give a new proof. Instead of Riesz product a new type of products based on Rademacher functions is used. Such Rademacher systems on metrizable non-discrete locally compact groups were introduced by the first-named author [Boll. Unione Mat. Ital., VII. Ser., A 4, 331-341 (1990; Zbl 0718.43001)]. So the dual group is not needed for the definition of the Rademacher functions and hence for the construction of the measures. Whence the existence of singular measures with absolutely continuous convolution squares on arbitrary nondiscrete locally compact groups follows.