query: Measure of infinite intersection of a decreasing sequence of set
positive_passages.docid: 153424
positive_passages.text: Proof of "continuity from above" and "continuity from below" from the axioms of probability
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 44623
negative_passages.text: Closed set as a countable intersection of open sets
negative_passages.docid: 141895
negative_passages.text: Proving that a sequence is monotone
negative_passages.docid: 133886
negative_passages.text: Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
negative_passages.docid: 69534
negative_passages.text: Measure of the Cantor set plus the Cantor set
negative_passages.docid: 5215
negative_passages.text: Can the principle of inclusion/exclusion be used to count elements in the intersection of a sequence of sets?
negative_passages.docid: 128482
negative_passages.text: The set of subsequential limits is closed
negative_passages.docid: 53363
negative_passages.text: Ultralimit of an eventually constant generalized sequence
negative_passages.docid: 103383
negative_passages.text: Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
negative_passages.docid: 154796
negative_passages.text: Completeness of sequence of reals with finitely many nonzero terms
negative_passages.docid: 130981
negative_passages.text: Co-countable measure on uncountable set
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 24050
negative_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 55648
negative_passages.text: Intersection of finite number of compact sets is compact?
negative_passages.docid: 21176
negative_passages.text: Closure of the set in dictionary order topology.
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval