On a Theorem of Carey and Pincus

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ARTICLE NO.

202, 1101 Ž1996.

0362

CORRIGENDUM Volume 145, Number 2 Ž1990., in the article ‘‘On a Theorem of Carey and Pincus,’’ by James S. Howland, pages 562]565: the Lemma and construction of m ˜ are correct, but the proof is not correct as it stands, since if the lower semicontinuous function F˜Ž l. were bounded on a set of full measure, it would be bounded everywhere. The point is that the choice of a n controls only the tail of F˜Ž l.. The argument on page 564 should therefore be emended as follows: On line 5, observe that lim inf K n has measure 1. Lines 10]15 should be replaced by the observation that if l g lim inf K n , then for some n s nŽ l., `

Ý

a j Fj Ž l . F

jsn

`

Ý jsn

1 2j

F1

so that F˜Ž l. is finite. The author thanks Barry Simon for pointing out the gap.

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