On the Absolute Convergence of Fourier–Haar Series in the Metric of Lp(0, 1), 0 < p < 1

Abstract

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.