A converse to a theorem of Salem and Zygmund

By proving a converse to a theorem of Salem and Zygmund the paper gives a full description of the sets E of points x   where the integral ∫01(F(x+t)−F(x−t))/tdt is infinite for a continuous and nondecreasing function F. It is shown that for this it is necessary and sufficient that E   is a GδGδ set of zero logarithmic capacity. Several corollaries are derived concerning boundary values of univalent functions.