Is there a decreasing sequence of sets in $\mathbb{R}^{n}$ with these outer-measure properties?

real-analysis examples-counterexamples measure-theory lebesgue-measure outer-measure

Instead of considering one Vitali set, consider all of them: $\{V_q: q ∈ ℚ\}$ and put $E_n := ⋃\{V_{q_k}: k ≥ n\}$ where $ℚ =: \{q_n: n ∈ ℕ\}$.

Related

$Z$ has a standard normal distribution. $P(Z \in (-a,b)) = 0.95$ where $a,b > 0$. Find the derivative the length, $l$, of the interval $(-a,b)$.
The field of constants of a differential ring. Derivative of real and complex numbers.
Prove that a bounded $f$ is integrable if $I_0 := \lim_{n\to\infty}L(f,P_n) = \lim_{n\to\infty}U(f,P_n)$
Why is $x^2\sin(1/x)$ not strictly differentiable?
How to solve $x^x=100$?
There exists a positive real number $u$ such that $u^3 = 3$
Hartshorne Exercise II.6.9(a): Picard group of a singular curve
Is it true that for a Group $G$ with Normal Group $N: G/N = GN/N$?
Using Leibniz's Rule to Evaluate Integrals
Prove that d(A,B)=0 iff Cl(A)∩B is non empty [duplicate]
Converting piecewise functions into single expressions
Show that for a symmetric positive-definite matrix we can write $A = D B D$ [closed]