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Topic: Borel Set for teapots

Explain to a teapot on fingers about https://en.m.wikipedia.org/wiki/Borel_set that its essence and in application to probability samplings. Thanks.

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Re: Borel Set for teapots

Hello, Mr Bombastic, you wrote: MB> Explain to a teapot on fingers about https://en.m.wikipedia.org/wiki/Borel_set that its essence and in application to probability samplings. MB> thanks. If it is short, shorted  the set (algebra) is probability measure definition range. If it is sensitive more in detail: the Set of Borelja constructed on set X-> this set from the subsets X, constructed by means of a finite amount of union operations and addition. The set of Borelja shorted concerning these operations - a sigma-algebra. Algebra elements (X) form subsets of set measurable space, i.e. On them can be hung  with number which is formed by certain rules (nonnegativity, 0 for empty set, it is added at join of non-overlapping sets) In  there is a space of events (set of all possible outcomes), on it the sigma-algebra (this Borelevsky set) is under construction, its measure (probability) is connected to each of which elements.

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Re: Borel Set for teapots

Hello, Mr Bombastic, you wrote: MB> Explain to a teapot on fingers about https://en.m.wikipedia.org/wiki/Borel_set that its essence and in application to probability samplings. MB> thanks. I, of course, do not claim for severity, but in my understanding the Borelevsky sigma-algebra (so it in Russian name) is a dial-up of sets in some space, shorted concerning union operations, intersection (and not only finite, but also countable) and additions. I.e. if 2 sets belong to it their join, intersection and additions (to the full space) too belong to it... These sets - . And it is necessary to enter a probability measure. The Borelevsky sigma-algebra is the most natural object for dial-up introduction  probability theory axioms. I.e. if to enter a probability measure on  sets all derived sets about which there is a speech in axioms, exist and too are .

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Re: Borel Set for teapots

Hello, Mr Bombastic, you wrote: MB> Explain to a teapot on fingers about https://en.m.wikipedia.org/wiki/Borel_set that its essence and in application to probability samplings. Well I would tell so: it is certain   on which it is already possible to construct  axiomatics (it if about ). I.e. numbers should be not mandatory (there can be an eagle-reshka as at a coin), many requirements, enough certain minimum are not necessary that all turned out.