The equivalence of two definitions of capacity

Adams, David R.; Polking, John C.

doi:10.1090/S0002-9939-1973-0328109-5

The equivalence of two definitions of capacity
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by David R. Adams and John C. Polking PDF

Proc. Amer. Math. Soc. 37 (1973), 529-534 Request permission

Abstract:

It is shown that two definitions for an ${L_p}$ capacity $(1 < p < \infty )$ on subsets of Euclidean ${R^n}$ are equivalent in the sense that as set functions their ratio is bounded above and below by positive finite constants. The classical notions of capacity correspond to the case $p = 2$.

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Application du théorème minimax a l’étude diverse capacités

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