ON THE ABSOLUTE CONVERGENCE OF FOURIER-HAAR SERIES IN THE METRIC OF L~p (0,1), 0 < 1

摘要

It is proved that for every ∈ > 0 there exists a measurable set E ⊂ [0,1] with measure |E| > 1 — ∈ such that for every function f(x) ∈ L[0,1] one can find a function g(x) ∈ L[0,1] coinciding with f(x) on E such that its Fourier-Haar series absolutely converges in the metric of L~p (0,1), 0 < p < 1. Bibliography: 30 titles.