On divergence of Fourier–Walsh series of continuous function (Անընդհատ ֆունկցիայի Ֆուրիե–Ուոլշի շարքի տարամիտության մասին)

Abstract

We prove that for any perfect set P of positive measure, for which 0 is a density point, one can construct a function f(x) continuous on [0,1) such that each measurable and bounded function, which coincides with f(x) on the set P has diverging Fourier–Walsh series at 0.