### Some articles on *set, borel, borel sets, sets*:

Borel Determinacy Theorem - Background - Topology

... For a given

... For a given

**set**A, whether a subset of Aω will be determined depends to some extent on its topological structure ... For the purposes of Gale–Stewart games, the**set**A is endowed with the discrete topology, and Aω endowed with the resulting product topology, where Aω is ... In particular, when A is the**set**{0,1}, the topology defined on Aω is exactly the ordinary topology on Cantor space, and when A is the**set**of natural numbers, it is ...Haar Measure - Haar's Theorem

... a unique countably additive, nontrivial measure μ on the

... a unique countably additive, nontrivial measure μ on the

**Borel**subsets of G satisfying the following properties The measure μ is left-translation-invariant μ(gE) = μ(E ... The measure μ is finite on every compact**set**μ(K) < ∞ for all compact K The measure μ is outer regular on**Borel sets**E The measure μ is inner ... properties that μ(U) > 0 for every non-empty open**Borel**subset U ...Descriptive Set Theory -

... Classical descriptive

**Borel Sets**- Regularity Properties of**Borel Sets**... Classical descriptive

**set**theory includes the study of regularity properties of**Borel sets**... For example, all**Borel sets**of a Polish space have the property of Baire and the perfect**set**property ... Modern descriptive**set**theory includes the study of the ways in which these results generalize, or fail to generalize, to other classes of subsets of Polish spaces ...Infinity-Borel Set - Incorrect Definition

... description at the top of this article as claiming that the ∞-

... description at the top of this article as claiming that the ∞-

**Borel sets**are the smallest class of subsets of containing all the open**sets**and closed under ... That is, one might wish to dispense with the ∞-**Borel**codes altogether and try a definition like this For each ordinal α define by transfinite recursion Bα as follows B0 is ... For a given even ordinal α, Bα+1 is the union of Bα with the**set**of all complements of**sets**in Bα ...### Famous quotes containing the word sets:

“It is odd but agitation or contest of any kind gives a rebound to my spirits and *sets* me up for a time.”

—George Gordon Noel Byron (1788–1824)

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