query: Every Lebesgue measure $0$ set in $\mathbb R$ has a disjoint translation
positive_passages.docid: 152310
positive_passages.text: If $E$ has Lebesgue measure $0$, must there exist a translate such that $E\cap E+x=\varnothing$?
negative_passages.docid: 136795
negative_passages.text: A non-measurable set of given outer measure
negative_passages.docid: 47096
negative_passages.text: translation invariant of integral on $\mathbb{R}$
negative_passages.docid: 60053
negative_passages.text: Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
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: 98717
negative_passages.text: Are all measure zero sets measurable?
negative_passages.docid: 137099
negative_passages.text: Lebesgue measure of the set of zeroes of Brownian motion
negative_passages.docid: 53663
negative_passages.text: outer measure and measurable sets
negative_passages.docid: 127575
negative_passages.text: Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
negative_passages.docid: 51260
negative_passages.text: Sum of sets of measure zero
negative_passages.docid: 98098
negative_passages.text: Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.
negative_passages.docid: 82236
negative_passages.text: Extension of the Lebesgue measurable sets
negative_passages.docid: 27615
negative_passages.text: Prove Borel Measurable Set A with the following property has measure 0.
negative_passages.docid: 60032
negative_passages.text: If the measure of union = sum of outer measures, then the sets are measurable
negative_passages.docid: 20810
negative_passages.text: Boundary of Ball of radius R has zero measure
negative_passages.docid: 90540
negative_passages.text: What is wrong in this proof: That $\mathbb{R}$ has measure zero
negative_passages.docid: 132382
negative_passages.text: Showing a set is nowhere dense in $C([0,1])$