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Order-two density and the strong law of large numbers
Published online by Cambridge University Press: 26 February 2010
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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
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- Copyright © University College London 1996
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