Question

Define exterior measure of $ECR^{d}$ and show that exterior measure iscountably subadditive.

Answer 1

The existence of this cover follows from definition of μ∗μ∗ as an infimum (since μ∗(An)<μ∗(An)+ε2μ∗(An)<μ∗(An)+ε2). Note that the set {∑∞n=1τ(Tn):Tn∈T,A⊂⋃∞n=1Tn}{∑n=1∞τ(Tn):Tn∈T,A⊂⋃n=1∞Tn} is not empty since the whole space cover AA and we can let (Tn)(Tn) be a constant sequence of sets being equal to the spacer (