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SOME RELATIONS BETWEEN PACKING PREMEASURE AND PACKING MEASURE

Published online by Cambridge University Press:  01 November 1999

DE-JUN FENG ,
SU HUA  and
ZHI-YING WEN
DE-JUN FENG
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, 100084, P. R. China Center for Advanced Study, Tsinghua University, Beijing, 100084, P. R. China
SU HUA
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, 100084, P. R. China
ZHI-YING WEN
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, 100084, P. R. China Department of Mathematics, Wuhan University, Wuhan, 430072, P. R. China
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Abstract

Let K be a compact subset of ℝn, 0[les ]s[les ]n. Let Ps0, [Pscr ]s denote s-dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between Ps0 and [Pscr ]s. We prove: if Ps0(K)<∞, then [Pscr ]s(K) = Ps0(K); and if Ps0(K) = ∞, then for any ε>0, there exists a compact subset F of K such that [Pscr ]s(F) = Ps0(F) and [Pscr ]s(F)[ges ] [Pscr ]s(K)−ε.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 6 , November 1999 , pp. 665 - 670
Copyright
© The London Mathematical Society 1999

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