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Published online by Cambridge University Press: 20 November 2018
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?