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- W2198555917 abstract "Recall the definition of a Borel set. If ℌ is any collection of subsets of a set X, there is a ionique smallest σ-field of subsets of X containing ℌ : the a-field generated by ℌ . (The notion of a field of sets was defined in Problem I.1. A field, F , of subsets of X is called a σ-field iff whenever An ∊ F , n = 1,2,..., then (bigcuplimits_{n = 1}^infty {{text{A}}_{text{n}} in F}) and (bigcaplimits_{n = 1}^infty {{text{A}}_{text{n}} in F})) In ℝ, the σ-field generated by the collection of open sets is the σ-field of all Borel sets: a subset of ℝ is a Borel set iff it is a member of this a-field. We show that the Borel sets lie in a ramified hierarchy, and that there are precisely ({text{2}}^{{{aleph}}_{text{0}} }) many Borel sets." @default.
- W2198555917 created "2016-06-24" @default.
- W2198555917 creator A5086950937 @default.
- W2198555917 date "1979-01-01" @default.
- W2198555917 modified "2023-09-27" @default.
- W2198555917 title "Some Topics in Pure Set Theory" @default.
- W2198555917 doi "https://doi.org/10.1007/978-1-4684-0084-7_4" @default.
- W2198555917 hasPublicationYear "1979" @default.
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