Borel Measure

Carlos S. Kubrusly
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 11 in Essentials of Measure Theory, 2015, pp 201-222 from Springer

Abstract: Abstract A topological space was defined in Problem 1.12: a set equipped with a topology. A topology on a set X is a collection $$\mathcal{T}$$ of subsets of X satisfying the following axioms: (i) the whole set X and the empty set $$\varnothing$$ lie in $$\mathcal{T}\!$$ , (ii) finite intersections of sets in $$\mathcal{T}$$ lie in $$\mathcal{T}\!$$ , and (iii) arbitrary unions of sets in $$\mathcal{T}$$ lie in $$\mathcal{T}\!$$ . The sets in $$\mathcal{T}$$ are called the open sets of X (with respect to $$\mathcal{T}$$ ).

Keywords: Topological Space; Borel Measure; Hausdorff Space; Finite Measure; Countable Union (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-22506-7_11

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