# Sigma algebra generated by partition

**Generated**

**Sigma-algebra**(B) Let X be a set and B a non-empty collection of subsets of X . The smallest

**algebra**containing all the sets of B is denoted (B ) and is called the

**sigma-algebra**

**generated**by the collection B . The term smallest here means that any

**sigma-algebra**containing the sets of B would have to contain all the sets of (B ) as well..

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**Algebra**and Its Applications. Phat Duong. pavan kumar + 25 More. Download Download PDF. Full PDF Package Download Full PDF Package. This Paper. A short summary of this paper. 28 Full PDFs related to this paper. Read Paper. Download Download PDF.

**generated**

**by**fx ng 2Z, f ng , and C. The free field realization of the Ding{Iohara{Miki

**algebra**is known as follows In the follo-wing, let q;t2C and we assume jqj<1. First we define the

**algebra**Bof bosons to be an associative C-algebra

**generated**

**by**fa ng 2Znf0gand the relation [a m;a n] = m 1 qjmj 1 tjmj m+n;0; m.

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**Generated**σ-

**algebra**. The smallest σ-

**algebra**that contains a given family of sets, see

**Generated**σ-

**algebra**(by sets) The smallest σ-

**algebra**that makes a function measurable or a random variable, see

**Sigma**-

**algebra**#σ-

**algebra**

**generated**by a function. This disambiguation page lists articles associated with the title

**Generated**σ-

**algebra**..

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**partition**of X we have that B = X − A, and so we see that A is closed under complements. A is closed under countable unions, in fact A is finite, so we only need to check that it is closed under finite unions.