Isomorphic measures on compact groups

BY S. Grekas

(Volume112 (1992), 349–360)

There is a gap in the proof of Theorem 5·8 of that paper. More precisely, it is not clear that the image of a completion regular measure under the map f of Lemma 5·7 is also completion regular, as f does not seem to preserve Borel measurability. Consequently, the proof of Theorems 5·A, 5·B and 5·C is not correct. However, in Remarks 5·13 there is a proof of Theorem 5·A using an alternative method. Thus, atleast Theorem 5-A is correct. The author believes that an analogous method can similarly be applied to Theorems 5·B and 5·C as well.

Invariance principles for logarithmic averages

By Miklos Csorgo and Lajos Horvath

(Volume112 (1992), 195–205)

In (1·4) and (1·5) of the paper above nt should be replaced by nt. Also, in the inequalities of (2·5) and (2·6) the expression should be replaced by

We are indebted and grateful to Professor Endre Csáki for pointing out these mistakes to us.