Rearrangements and category

Abstract

Kolmogorov stated, and Zahorski proved, that there exists an L 2 -Fourier series such that some rearrangement of it diverges almost everywhere. Kac and Zygmund asked if the set of rearrangements which make this Fourier series diverge almost everywhere is first category or second category. A general theorem is proved which has as a special case that the set of rearrangements in question is residual.