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A Local Property of Measurable Sets

Published online by Cambridge University Press:  20 November 2018

W. Eames
W. Eames*
Affiliation:
Queen's University and Sir John Cass College
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Let Ω be a metric space with metric ρ, let C be a class of closed sets from Ω and let τ be a non-negative real-valued set function on C. We assume that the empty set ϕ is in C and that τ(I)= 0 if and only if I = ϕ. For each set A in Ω, we define φ(A), 0 ≤ φ(A) ≤ ∞ by:

where the infimum is taken for all possible countable collections of sets I(n) from C such that:

and the diameter of I(n), d(I(n)), is less than ∈ for every n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 632 - 640
Copyright
Copyright © Canadian Mathematical Society 1960

References

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