If $f$ and $g$ are measurable and well-defined a.e., show $f+g$ is measurable.
96286
Proving that sum of two measurable functions is measurable.
98474
Show the existence of a certain subgroup of F2
134368
In Group theory proofs what is meant by "well defined"
98098
Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.
53425
Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
19632
Intuition behind the definition of a measurable set
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
34542
If $f$ is integrable then $|f|$ is also integrable
89514
Show that if $g \circ f$ is injective, then so is $f$.
126698
measurability of a function -equivalent conditions
7681
How can this theorem about weakly measurable functions on $\sigma$-finite measure spaces be deduced from the finite measure space case?
75479
Proving that this function is continuous on $G\times G$
24777
If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$?
65334
Show that a certain set is measurable
6450
Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?