Note on a Theorem of Myrberg*

On p. 421, line 30, of that note I remark “δ(x) is a lower semi-continuous function of x”. That statement is, in general, untrue. The proof should rather run as follows:

The subset of E1 where δ(x) ≥ a > 0 is clearly closed and, as α tends to 0, tends to h−mE1. Hence, by taking α sufficiently small, we find a closed subset of E1, of positive h-measure, every point x of which has the property that

whenever 0 < d ≤ α. We may call this subset again E1 and the proof, from the top of p. 422, goes as before.