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Order-two density and the strong law of large numbers

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

J. M. Marstrand
J. M. Marstrand
Affiliation:
School of Mathematics, University Walk, Bristol. BS8 1TW
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Throughout this paper we assume that k is a given positive integer. As usual, B(x, r) denotes the closed ball with centre at x∈ℝk and radius r > 0. Let μ be a Radon measure on ℝk, that is, μ is locally finite and Borel regular. For s ≥ 0, the lower and upper s–dimensional densities of μ at x are denned respectively by

and

MSC classification

Secondary: 28A78: Hausdorff and packing measures

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Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 1 - 22
Copyright
Copyright © University College London 1996

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