Proving measurable function: Real versus rational number
57581
Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)>c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?
125910
Continuity of Integration for a measurable function
92638
Approximation of measurable function by simple functions
19632
Intuition behind the definition of a measurable set
88418
Proof of a theorem saying that we can make a measurable function continuous by altering it by a set of arbitarily small measure
158309
Find a function that is continuous only on rationals
43268
How to prove that the set of rational numbers are countable?
82236
Extension of the Lebesgue measurable sets
58827
Absolute value of a measurable function is measurable
30478
How to prove that a number is irrational
70409
Rational Equivalence Relation and Measure
87216
Lebesgue non-measurable function
91126
A question about Measurable function
2269
Proof that the real numbers are countable: Help with why this is wrong
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
56464
Proving the irrationality of $e^n$
53663
outer measure and measurable sets