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On the construction of measures
Published online by Cambridge University Press: 26 February 2010
Extract
1. Given a metric space (X, ρ) a family of subsets of X which includes the empty set Ø, and a non-negative function τ on with τ(Ø)=0, an outer measure μ* may be defined by
where empty infimums have value +∞. It is easily seen that μ* is a metric outer measure [i.e., if ρ(A, B)>0 then μ*(A∪B)=μ*(A)+μ*(B)] and from this it follows that all Borel sets in X are μ*-measurable.
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- Copyright © University College London 1966