If a function is continuous a.e., then it is measurable.
122585
Show that a function almost everywhere continuous is measurable
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
158122
If $f$ is measurable, then support of $f$ is measurable?
56303
Why this definition for Lebesgue measurable functions?
151707
Fatou's lemma and measurable sets
69716
$f_x$ is Borel measurable and $f^y$ is continuous then $f$ is Borel measurable
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
12523
Supremum of a Continuous Function is Continuous
96099
Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.
59581
A function which is continuous in one variable and measurable in other is jointly measurable
125682
Proof verification: the product of two continuous functions is continuous
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
22597
Composition of measurable function and continuous function
9614
How does the existence of a limit imply that a function is uniformly continuous
1474
How to prove limit of measurable functions is measurable
98200
$E$ Lebesgue measurable implies $E^2$ Lebesgue measurable?
84512
The preimage of continuous function on a closed set is closed.