If $E$ is measurable and $0(1-\epsilon)m(I)$
65595
Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$
23946
Prove the definitions of $e$ to be equivalent
125910
Continuity of Integration for a measurable function
91126
A question about Measurable function
148555
Prove that every Lebesgue measurable function is equal almost everywhere to a Borel measurable function
143699
Bounded measurable function and integral with charcteristic function
118353
For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
126698
measurability of a function -equivalent conditions
84263
A Lebesgue measure question
144817
Proving Caratheodory measurability if and only if the measure of a set summed with the measure of its complement is the measure of the whole space.
43420
caratheodory measurability condition
76240
How is $\epsilon_0$ countable?
123132
Counterexample for a non-measurable function?
41683
Pre-image of a measurable set A is always measurable?
52545
Prove limit converges in definition of $e.$
94971
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x