Proving a set is Lebesgue Measurable
44270
$E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
18429
Counting measure proof
125910
Continuity of Integration for a measurable function
97841
General property regarding outer measure for a nested sequence of sets (measurable or not).
58827
Absolute value of a measurable function is measurable
41683
Pre-image of a measurable set A is always measurable?
47187
Proving the measure of an increasing sequence of measurable sets is the limit of the measures
88602
Inner regularity of Lebesgue measurable sets
98580
Lebesgue-measurable sets requiring the Axiom of Choice to construct
113778
Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
137099
Lebesgue measure of the set of zeroes of Brownian motion
96286
Proving that sum of two measurable functions is measurable.
84263
A Lebesgue measure question
158122
If $f$ is measurable, then support of $f$ is measurable?
156176
Lebesgue measurability of nearly identical sets
19452
Restriction of a Lebesgue integral to a subset of a measurable set.
98098
Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.