query: Are all Jordan measurable sets Borel?
positive_passages.docid: 17764
positive_passages.text: What's the relationship between Borel set and set whose boundary is measure zero?
negative_passages.docid: 69499
negative_passages.text: Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
negative_passages.docid: 97557
negative_passages.text: supremum of uncountable families of Borel measurable functions
negative_passages.docid: 19632
negative_passages.text: Intuition behind the definition of a measurable set
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 $m(E\setminus F)<\epsilon$
negative_passages.docid: 88714
negative_passages.text: Are there more general spaces than Euclidean spaces to have the Heine–Borel property?
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: 19452
negative_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 72050
negative_passages.text: Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure
negative_passages.docid: 74720
negative_passages.text: Is every set of measure zero countable?
negative_passages.docid: 14496
negative_passages.text: Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
negative_passages.docid: 32347
negative_passages.text: Limit of a decreasing sequence of measurable sets.
negative_passages.docid: 53425
negative_passages.text: Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
negative_passages.docid: 24749
negative_passages.text: Monotone functions and Borel sets
negative_passages.docid: 136795
negative_passages.text: A non-measurable set of given outer measure
negative_passages.docid: 52104
negative_passages.text: A pseudometric on the space of the measurable functions is complete
negative_passages.docid: 37361
negative_passages.text: Is there a measurable set $A$ such that $m(A \cap B) = \frac12 m(B)$ for every open set $B$?