query: Finite atomic measure space can be a countable disjoint union of atoms
positive_passages.docid: 153651
positive_passages.text: Countable partition in atoms
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 6210
negative_passages.text: Countable compact spaces as ordinals
negative_passages.docid: 21892
negative_passages.text: Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 135112
negative_passages.text: Outer measure of product of sets
negative_passages.docid: 136094
negative_passages.text: $G_\delta$ singletons in compact Hausdorff and first countability
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 97697
negative_passages.text: Countable union of sets of cardinality $c$ has cardinality $c$
negative_passages.docid: 125580
negative_passages.text: Proving that every countable metric space is disconnected?
negative_passages.docid: 40785
negative_passages.text: Finite signed measures and their boundedness
negative_passages.docid: 36315
negative_passages.text: Is $[0,1]$ a countable disjoint union of closed sets?
negative_passages.docid: 33207
negative_passages.text: Bases having countable subfamilies which are bases in second countable space
negative_passages.docid: 78225
negative_passages.text: Countable additivity implies countable subadditivity?
negative_passages.docid: 138202
negative_passages.text: Every open set in $\mathbb{R}$ is a countable union of closed sets
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 74720
negative_passages.text: Is every set of measure zero countable?