Let f,g be bounded measurable functions on a set E of finite measure. Show that: If f=a.e.g then ∫f=∫g
93965
Lebesgue integration: $f = g$ a.e. $ \Rightarrow \int_\Omega f = \int_\Omega g$
113122
Prove that a continuous real function with finite limits is bounded
121504
Supremum of a product measurable function...
74876
Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
7437
Converse of mean value theorem
72050
Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure
127919
prove that if $E$ is connected and $E \subseteq F \subseteq \overline{E}$, then $F$ is connected.
65334
Show that a certain set is measurable
91352
If $\Re(f)$ is bounded then f is constant.
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
82778
If a measure is semifinite, then there are sets of arbitrarily large but finite measure
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
9613
If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$
83665
Prove a assertion concerning Lebesgue space
66391
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
98897
Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
92638
Approximation of measurable function by simple functions