measurable set and complement in $[0,1]$
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure
119003
Complement of $c_{0}$ in $\ell^{\infty}$
151707
Fatou's lemma and measurable sets
120273
Showing that a collection of sets is a $\sigma$-algebra: either set or complement is countable
89719
Probability of selecting a non-measurable set
113227
Measure spaces are proper subsets
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
69534
Measure of the Cantor set plus the Cantor set
47056
Show that the boundary of a set equals the boundary of its complement
102250
Subset of $C[0,1]$ is nowhere dense
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
3023
Construction of a Borel set with positive but not full measure in each interval
19452
Restriction of a Lebesgue integral to a subset of a measurable set.
95294
Dense subset of $C[0,1]$ which preserves rationals
138055
If $A$ has a positive Lebesgue measure then there exist subsets which are not measurable
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
41683
Pre-image of a measurable set A is always measurable?