Does any subset of $[0,1]$ have a well-defined Lebesgue Measure? No.
100919
Examples of non-measurable sets in $\mathbb{R}$
45216
Cardinality of $[0,1]$
65595
Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$
57206
Lebesgue measure on probability measure
4111
Outer measure is countably subadditive
57462
Lebesgue Measure of the Graph of a Function
60032
If the measure of union = sum of outer measures, then the sets are measurable
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
77289
Example 2, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: If $X$ is a well ordered set, then $X \times [0, 1)$ is a linear continuum
3023
Construction of a Borel set with positive but not full measure in each interval
83665
Prove a assertion concerning Lebesgue space
87216
Lebesgue non-measurable function
154621
A set with a finite integral of measure zero?
69534
Measure of the Cantor set plus the Cantor set
130297
$A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
82778
If a measure is semifinite, then there are sets of arbitrarily large but finite measure
272
Cantor Sets/nonempty/cardinality