query: Lebesgue measurable simple function and its Borel measurable counterpart
positive_passages.docid: 148555
positive_passages.text: Prove that every Lebesgue measurable function is equal almost everywhere to a Borel measurable function
negative_passages.docid: 58827
negative_passages.text: Absolute value of a measurable function is measurable
negative_passages.docid: 94980
negative_passages.text: Measurable functions in a countable co-countable $\sigma$-algebra
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: 114947
negative_passages.text: Bounded variation implies Borel measurable
negative_passages.docid: 96286
negative_passages.text: Proving that sum of two measurable functions is measurable.
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: 52104
negative_passages.text: A pseudometric on the space of the measurable functions is complete
negative_passages.docid: 57206
negative_passages.text: Lebesgue measure on probability measure
negative_passages.docid: 19773
negative_passages.text: Is finite additivity a property of the Lebesegue outer measure?
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: 151707
negative_passages.text: Fatou's lemma and measurable sets
negative_passages.docid: 109301
negative_passages.text: Lebesgue Integral of Non-Measurable Function
negative_passages.docid: 63309
negative_passages.text: How to find a measurable but not integrable function or a positive integrable function?
negative_passages.docid: 158122
negative_passages.text: If $f$ is measurable, then support of $f$ is measurable?
negative_passages.docid: 98098
negative_passages.text: Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.