Lebesgue-measurable sets requiring the Axiom of Choice to construct
41937
Can one construct a non-measurable set without Axiom of choice?
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
78228
Hausdorff Maximal Principle and Axiom of Choice
115219
If $E$ is Lebesgue measurable, show that there exists a closed set $F$ with $F \subset E$ and $m(E\setminus F)<\epsilon$
17624
Axiom of Choice iff Every set has a choice function
92638
Approximation of measurable function by simple functions
83757
Is the following equivalent to the axiom of choice?
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
5313
Existence of how many sets is asserted by the axiom of choice in this case?
57206
Lebesgue measure on probability measure
144362
The construction of a Vitali set
70143
Mutually exclusive countable subsets of a countable set
138055
If $A$ has a positive Lebesgue measure then there exist subsets which are not measurable
84263
A Lebesgue measure question
132046
Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?
19632
Intuition behind the definition of a measurable set
19414
Uncountable subset with uncountable complement, without the Axiom of Choice