query: Not all sets in $\mathbb{R}$ are Lebesgue measurable sets
positive_passages.docid: 144362
positive_passages.text: The construction of a Vitali set
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: 60868
negative_passages.text: Interplay of Hausdorff metric and Lebesgue measure
negative_passages.docid: 72050
negative_passages.text: Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure
negative_passages.docid: 107160
negative_passages.text: Open Set and Measure Theory
negative_passages.docid: 128766
negative_passages.text: Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
negative_passages.docid: 113227
negative_passages.text: Measure spaces are proper subsets
negative_passages.docid: 88099
negative_passages.text: Not $\sigma$-compact set without axiom of choice
negative_passages.docid: 60032
negative_passages.text: If the measure of union = sum of outer measures, then the sets are measurable
negative_passages.docid: 147546
negative_passages.text: $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable
negative_passages.docid: 35713
negative_passages.text: Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|<|\mathbb{R}|$, is it true that $X$ is null?
negative_passages.docid: 136795
negative_passages.text: A non-measurable set of given outer measure
negative_passages.docid: 135548
negative_passages.text: Every section of a measurable set is measurable? (in the product sigma-algebra)
negative_passages.docid: 137203
negative_passages.text: Measurable cardinal existence condition
negative_passages.docid: 73619
negative_passages.text: Why is $(\mathbb{R}, \mathcal{P}(\mathbb{R}))$ called a measurable space when actually is not?
negative_passages.docid: 139612
negative_passages.text: Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
negative_passages.docid: 92571
negative_passages.text: Sets with no asymptotical density over $\mathbb N$