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Some Relations Between Packing Premeasure and Packing Measure

Some Relations Between Packing Premeasure and Packing Measure Let K be a compact subset of Rn, 0 ⩽ s ⩽ n. Let P0s, Ps denote s‐dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between P0s and Ps. We prove: if P0s(K)<∞, then Ps(K)=P0s(K); and if P0s(K)=∞, then for any ε > 0, there exists a compact subset F of K such that Ps(F)=P0s(F) and Ps(F) ⩾ Ps(K) − ε. 1991 Mathematics Subject Classification 28A80, 28A78. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Some Relations Between Packing Premeasure and Packing Measure

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References (6)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609399006256
Publisher site
See Article on Publisher Site

Abstract

Let K be a compact subset of Rn, 0 ⩽ s ⩽ n. Let P0s, Ps denote s‐dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between P0s and Ps. We prove: if P0s(K)<∞, then Ps(K)=P0s(K); and if P0s(K)=∞, then for any ε > 0, there exists a compact subset F of K such that Ps(F)=P0s(F) and Ps(F) ⩾ Ps(K) − ε. 1991 Mathematics Subject Classification 28A80, 28A78.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Nov 1, 1999

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