Do there exist any subsets of $\mathbb{R}$ with positive measure but not of size continuum?
35713
Let $X\subset \mathbb{R}$ Lebesgue measurable, $|X|<|\mathbb{R}|$, is it true that $X$ is null?
19773
Is finite additivity a property of the Lebesegue outer measure?
136795
A non-measurable set of given outer measure
33309
Subgroup of $\mathbb{R}$ either dense or has a least positive element?
82778
If a measure is semifinite, then there are sets of arbitrarily large but finite measure
104744
Can sets of cardinality $\aleph_1$ have nonzero measure?
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
134310
Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
65180
A compact Hausdorff space that is not metrizable
83166
Homeomorphism(topological spaces) version of Cantor–Bernstein–Schroeder theorem
132025
Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
92571
Sets with no asymptotical density over $\mathbb N$
131664
Why is any Lebesgue-Stieltjes measure on $(\mathbb{R},\mathcal{B}_\mathbb{R})$ not complete?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
100919
Examples of non-measurable sets in $\mathbb{R}$