Vol. 64, No. 1, 1976

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Derivation of the integrals of L(q)-functions

C. A. Hayes

Vol. 64 (1976), No. 1, 173–180
Abstract

It is known that if a derivation basis possesses Vitali-like covering properties, with covering families having arbitrarily small L(p)(μ)-overlap, where 1 p < +and μ is a σ-finite measure in an abstract measure space, then derives the μ-integrals of all functions f L(q)(μ) where p1 + q1 = 1 if p > 1; q = +if p = 1. The converse is well known for the case q = +, p = 1, and a partial converse is known for the case p > 1, if is a [U]-basis. The present paper offers a converse for p > 1 under general hypotheses and, simultaneously, removes the necessity that be a [U]-basis.

Mathematical Subject Classification 2000
Primary: 26A24
Secondary: 28A15
Milestones
Received: 19 June 1975
Revised: 2 April 1976
Published: 1 May 1976
Authors
C. A. Hayes