|
|||||
What is Borel Hierarchy?The Borel Hierarchy is a system for objectively deciding which subsets of a Polish space are superior to other ones and must be obeyed. It is defined using transfinite induction, with the base case Σ_1 = { the open sets }, Π_1 = { the closed sets }, and for a countable ordinal α, Σ_α is the collection of sets which are the countable union of sets appearing in Π_β for β < α, and dually, Π_α is the collection of sets which are the countable intersection of sets appearing in Σ_β for β < α. The Borel algebra is the σ-algebra generated by open sets, and it doesn't appear at any countable level of the Borel hierarchy; instead, it exists outside the countable hierarchy, with rank ω_1, the least uncountable ordinal, and it is a superset of all the other sets in the hierarchy. Borel Hierarchy - video |
|||||
www.Definder.net Powered by Urban Dictionary |