Some Relations Between Packing Premeasure and Packing Measure

Abstract

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