query: Let E be a measureable subset of [0,1] with positive measure. Let $E-E= \{ x-y | x,y \in E\}$Show that this set contains a neighborhood of 0.
positive_passages.docid: 60110
positive_passages.text: The set of differences for a set of positive Lebesgue measure
negative_passages.docid: 84359
negative_passages.text: On Lebesgue Outer Measure of an interval
negative_passages.docid: 155311
negative_passages.text: How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
negative_passages.docid: 60032
negative_passages.text: If the measure of union = sum of outer measures, then the sets are measurable
negative_passages.docid: 85818
negative_passages.text: $E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
negative_passages.docid: 47056
negative_passages.text: Show that the boundary of a set equals the boundary of its complement
negative_passages.docid: 84263
negative_passages.text: A Lebesgue measure question
negative_passages.docid: 47187
negative_passages.text: Proving the measure of an increasing sequence of measurable sets is the limit of the measures
negative_passages.docid: 93419
negative_passages.text: Let $\mathcal A$ be a collection of pairwise disjoint subsets of a $\sigma$-finite measure space,Show that $\mathcal A$ is at most countable.
negative_passages.docid: 24050
negative_passages.text: Characterization of the Closure of a Set
negative_passages.docid: 113778
negative_passages.text: Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 154559
negative_passages.text: For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
negative_passages.docid: 80827
negative_passages.text: Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
negative_passages.docid: 65595
negative_passages.text: Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$
negative_passages.docid: 103451
negative_passages.text: Show that $Y$ is locally compact.
negative_passages.docid: 55023
negative_passages.text: if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$