query: Intuition behind Caratheodory's definition for measurable sets?
positive_passages.docid: 19632
positive_passages.text: Intuition behind the definition of a measurable set
negative_passages.docid: 98897
negative_passages.text: Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
negative_passages.docid: 124779
negative_passages.text: Intuition for uniform continuity of a function on $\mathbb{R}$
negative_passages.docid: 97735
negative_passages.text: Continuous functions are differentiable on a measurable set?
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: 16667
negative_passages.text: How to get intuition in topology concerning the definitions?
negative_passages.docid: 89719
negative_passages.text: Probability of selecting a non-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: 19452
negative_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 138055
negative_passages.text: If $A$ has a positive Lebesgue measure then there exist subsets which are not measurable
negative_passages.docid: 123132
negative_passages.text: Counterexample for a 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: 88736
negative_passages.text: How does the Axiom of Extensionality prove the uniqueness of Specified sets?
negative_passages.docid: 88602
negative_passages.text: Inner regularity of Lebesgue measurable sets
negative_passages.docid: 69857
negative_passages.text: Is the set $A=\{x\in E|\lim_{n \to\infty} f_n(x)\ exists\ (finitely)\}$ measurable?
negative_passages.docid: 26246
negative_passages.text: Why does a Lipschitz function $f:\mathbb{R}^d\to\mathbb{R}^d$ map measure zero sets to measure zero sets?
negative_passages.docid: 122758
negative_passages.text: Are Monotone functions Borel Measurable?