query: clear example of sigma algebra generated by r.v
positive_passages.docid: 144359
positive_passages.text: A random variable that induces a $\sigma$-algebra the same as the one in the sample space
negative_passages.docid: 81327
negative_passages.text: union of sigma algebra is sigma algebra
negative_passages.docid: 73382
negative_passages.text: A concrete example of involution in group theory
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
negative_passages.docid: 103307
negative_passages.text: Generate the smallest $\sigma$-algebra containing a given family of sets
negative_passages.docid: 101095
negative_passages.text: Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
negative_passages.docid: 47015
negative_passages.text: Vector Space Structures over ($\mathbb{R}$,+)
negative_passages.docid: 63218
negative_passages.text: Is conditional expectation with respect to two sigma algebra exchangeable?
negative_passages.docid: 20581
negative_passages.text: How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
negative_passages.docid: 157599
negative_passages.text: what is the meaning of $F_\sigma$ and $G_\delta?$
negative_passages.docid: 86622
negative_passages.text: I want to find an example where the Spectrum is equal to the Continuous Spectrum in C[0,1]; $\sigma_c(A)=\sigma(A)$
negative_passages.docid: 139622
negative_passages.text: Generator of rational functions unchanged under $\sigma(X) = X + 1$
negative_passages.docid: 120442
negative_passages.text: Prove Borel sigma-algebra translation invariant
negative_passages.docid: 146006
negative_passages.text: Uncountable $\sigma$-algebra
negative_passages.docid: 35140
negative_passages.text: Existence of minimal $\sigma$-algebra and transfinite induction
negative_passages.docid: 112216
negative_passages.text: Geometric description of canonical commutation relation
negative_passages.docid: 47159
negative_passages.text: Wanted: example of an increasing sequence of $\sigma$-fields whose union is not a $\sigma$-field