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Packing measures, packing dimensions, and the existence of sets of positive finite measure

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A Packing Problem for Measurable Sets

Canadian Journal of Mathematics, 1967
Given a probability measure space (Ω,,P)consider the followingpacking problem.What is the maximum number,b(K,Λ), of sets which may be chosen fromso that each set has measureKand no two sets have intersection of measure larger than Λ <K?In this paper the packing problem is solved for any non-atomic probability measure space. Rather than obtaining the
Sankoff, D., Dawson, D. A.
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Hausdorff and packing measure for solenoids

Ergodic Theory and Dynamical Systems, 2003
Summary: We prove that the solenoid with two different contraction coefficients has zero Hausdorff and positive packing measure in its own dimension and the SBR measure is equivalent to the packing measure on the attractor. Further, we prove similar statements for Slanting Baker maps with intersecting cylinders (in \(\mathbb{R}^{2}\)).
Rams, Michał, Simon, Károly
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Some Relations Between Packing Premeasure and Packing Measure

Bulletin of the London Mathematical Society, 1999
Summary: Let \(K\) be a compact subset of \(\mathbb{R}^n\), \(0\leq s\leq n\). Let \(P^s_0\), \({\mathcal P}^s\) denote \(s\)-dimensional packing premeasure and measure, respectively. We discuss in this paper the relation between \(P^s_0\) and \({\mathcal P}^s\). We prove: if \(P^s_0(K)< \infty\), then \({\mathcal P}^s(K)= P^s_0(K)\); and if \(P^s_0(K)=
Feng, De-Jun, Hua, Su, Wen, Zhi-Ying
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The Packing Theorem and Packing Measure

Mathematische Nachrichten, 1990
AbstractFor a VITALI class of a metric space (X, d) a packing measure is introduced following the ideas of [7]. The Packing Theorem of VITALI is a powerful mean to derive density results for measures [1, 2, 3]. Conversely, the notion of packing measure allows us to give sufficient conditions for a measure that the packing theorem of VITALI hods.
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Packing Measure and Dimension of Random Fractals

Journal of Theoretical Probability, 2002
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Berlinkov, Artemi, Mauldin, R. Daniel
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Packing Measure Analysis of Harmonic Measure

Journal of the London Mathematical Society, 1995
We prove a conjecture of James Taylor that for any simply connected domain \(\Omega \subset R^2\) there is a subset \(E \subset \partial \Omega\) of full harmonic measure such that \(E\) has packing dimension 1. The results of Markov ensure that there exists a subset \(E\) of full harmonic measure with Hausdorff dimension 1.
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Some Measure-Theoretic Properties of Packing Measure

Periodica Mathematica Hungarica, 1998
This paper is an informal discussion of some fundamental measure-theoretic differences between the families of measures known as packing measures and Hausdorff measures. Two main issues of focus are, whether or not a set of infinite measure necessarily contains a subset of positive finite measure, and the question of Borel regularity.
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Comparing Packing Measures to Hausdorff Measures on the Line

Mathematische Nachrichten, 2002
In this paper the author compare packing measures to Hausdorff measures on the line. The main result of this paper is as follows.
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