Vol. 79, No. 2, 1978

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ISSN: 0030-8730
Quasi-additivity and sets of finite Lp-capacity

David R. Adams

Vol. 79 (1978), No. 2, 283–291
Abstract

The Bessel Lp-capacity of order α > 0, Bα,p, and the Riesz Lp-capacity of order α, Rα,p, are shown to have the same sets of finite capacity in Euclidean Rn, αp < n. However, they have markedly different behavior as countably “almost” additive (quasi-additive) set functions - i.e., as applied to sets that are partitioned by increasing concentric rings.

Mathematical Subject Classification 2000
Primary: 31B15
Secondary: 46E35
Milestones
Received: 15 February 1978
Published: 1 December 1978
Authors
David R. Adams