Quasi-additivity and sets of finite L^p-capacity

David R. Adams

Vol. 79 (1978), No. 2, 283–291

DOI: 10.2140/pjm.1978.79.283

Abstract

The Bessel L^p-capacity of order α > 0, B_α,p, and the Riesz L^p-capacity of order α, R_α,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