query: Is $\bigcup_{i = 1}^\infty \mathcal{A}_i$ necessarily a $\sigma$-algebra?
positive_passages.docid: 19996
positive_passages.text: Example where union of increasing sigma algebras is not a sigma algebra
negative_passages.docid: 67637
negative_passages.text: How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$?
negative_passages.docid: 129243
negative_passages.text: Is $C_{c}^{\infty}[a,b]$ a complete metric space?
negative_passages.docid: 35140
negative_passages.text: Existence of minimal $\sigma$-algebra and transfinite induction
negative_passages.docid: 147783
negative_passages.text: Showing a sigma algebra is the union of certain collection of sigma algebras
negative_passages.docid: 115120
negative_passages.text: Finite dimensional $C^*$-algebras
negative_passages.docid: 31617
negative_passages.text: Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?
negative_passages.docid: 20789
negative_passages.text: If $\Sigma \vdash \varphi$ then $\Sigma \vdash \forall x \varphi$. Why when $(\varphi \implies \forall x \varphi)$ is not true?
negative_passages.docid: 79734
negative_passages.text: Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
negative_passages.docid: 7681
negative_passages.text: How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
negative_passages.docid: 14861
negative_passages.text: If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer
negative_passages.docid: 94980
negative_passages.text: Measurable functions in a countable co-countable $\sigma$-algebra
negative_passages.docid: 55157
negative_passages.text: $\sigma$-algebras on a countable set is generated by partitions of the set
negative_passages.docid: 14647
negative_passages.text: Conditional expectation on more than one sigma-algebra
negative_passages.docid: 38963
negative_passages.text: Ideals in ring of continuous functions $\mathcal{C}[0,1]$ ... NBHM- Algebra
negative_passages.docid: 134983
negative_passages.text: Borel sigma algebra not containing all subsets of $\mathbb{R}$?
negative_passages.docid: 135548
negative_passages.text: Every section of a measurable set is measurable? (in the product sigma-algebra)