Question: Let E Rn. The translation of E by an x Rn is the set x + E = {y Rn: y =

Let E ⊂ Rn. The translation of E by an x ∈ Rn is the set x + E = {y ∈ Rn: y = x + z for some z ∈ E}, and the dilation of E by a scalar a > 0 is the set aE = {y ∈ Rn: y = az for some z ∈ E}.
a) Prove that E is a Jordan region if and only if x + E is a Jordan region, in which case Vol(x + E) = Vol(E).
b) Prove that E is a Jordan region if and only if a E is a Jordan region, in which case Vol(aE) = anVol(E).

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