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In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets. Each Borel set is assigned a unique countable ordinal number called the rank of the Borel set. The Borel hierarchy is of particular interest in descriptive set theory. One common use of the Borel hierarchy is to prove facts about the Borel sets using transfinite induction on rank. Properties of sets of small finite ranks are important in measure theory and analysis. == Borel sets == (詳細はPolish space then there are many sets that are not Borel. * If the space is a countable set with the discrete topology then every subset is Borel. --> 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Borel hierarchy」の詳細全文を読む スポンサード リンク
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