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A Packing Problem for Measurable Sets
Published online by Cambridge University Press: 20 November 2018
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Given a probability measure space (Ω, 
, P) consider the following packing problem. What is the maximum number, b(K, Λ), of sets which may be chosen from so that each set has measure K and 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 solution explicitly, however, it is convenient to solve the following minimal paving problem. In a non-atomic a-finite measure space (Ω, , μ) what is the measure, V(b, K, Λ), of the smallest set which is the union of exactly b subsets of measure K such that no subsets have intersection of measure larger than Λ?
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- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 1967
References
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Ryser, H. J., Combinatorial mathematics, Carus Mathematical Monograph No. 14 (1963).Google Scholar
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