query: Characterization of (Lebesgue) measurable sets
positive_passages.docid: 144817
positive_passages.text: Proving Caratheodory measurability if and only if the measure of a set summed with the measure of its complement is the measure of the whole space.
negative_passages.docid: 60110
negative_passages.text: The set of differences for a set of positive Lebesgue measure
negative_passages.docid: 128332
negative_passages.text: Counterexample to "Measurable in each variable separately implies measurable"
negative_passages.docid: 97557
negative_passages.text: supremum of uncountable families of Borel measurable functions
negative_passages.docid: 126698
negative_passages.text: measurability of a function -equivalent conditions
negative_passages.docid: 25306
negative_passages.text: A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset
negative_passages.docid: 26369
negative_passages.text: Proving seemingly obvious equations with measure theory
negative_passages.docid: 93684
negative_passages.text: Show that $\mu (E \setminus A)>0$ if $A$ is a nonmeasurable subset of $X$ and $A \subseteq E$, $E$ is measurable.
negative_passages.docid: 22558
negative_passages.text: Vitali-type set with given outer measure
negative_passages.docid: 112323
negative_passages.text: Showing that $f = 0 $ a.e. if for any measurable set $E$, $\int_E f = 0$
negative_passages.docid: 27615
negative_passages.text: Prove Borel Measurable Set A with the following property has measure 0.
negative_passages.docid: 113227
negative_passages.text: Measure spaces are proper subsets
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: 135656
negative_passages.text: Why non-measurable sets exist?
negative_passages.docid: 98717
negative_passages.text: Are all measure zero sets measurable?
negative_passages.docid: 137203
negative_passages.text: Measurable cardinal existence condition
negative_passages.docid: 115219
negative_passages.text: If $E$ is Lebesgue measurable, show that there exists a closed set $F$ with $F \subset E$ and $m(E\setminus F)<\epsilon$