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For \(\Q =\{Q_n:n∈ℕ\}\) is \[ \bigcup \Q = \bigcup _{n=1}^∞ Q_n ? \]
For \(x,y∈ℝ^d\) and \(i∈\{1,…,d\}\) is it true, that \(x_i+y_i=(x+y)_i\)?
Is it true for all \(x∈ℝ\) that \((x+∞)-∞=x+(∞-∞)\)?
In \(ℝ\), what is the value of \(\lmo {\{2\}}?\)
Is it true for any set of cubes \(Q_1,…,Q_n⊂ℝ^d\) that \[ \lmo {Q_1∪…∪Q_n} = \lmo {Q_1}+…\lmo {Q_n} ? \]
Let \(μ_*\) be an outer measure on \(Ω\). Is it true for all sets \(A,B⊂Ω\) that \(μ_*(A∪B)\leqμ _*(A)+μ_*(B)\)?
Let \(μ_*\) be an outer measure on \(Ω\). Is it true for all sets \(A,B⊂Ω\) with \(A∩B=∅\) that \(μ_*(A∪B)=μ_*(A)+μ_*(B)\)?
Let \(μ_*\) be an outer measure on \(Ω\). Is it true for all measurable sets \(A,B⊂Ω\) with \(A∩B=∅\) that \(μ_*(A∪B)=μ_*(A)+μ_*(B)\)?
Does Lebesgue outer measure assign a number to every subset \(E⊂ℝ^d\)? Does this number always represent a reasonable notion of volume of the set?