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1. Suppose f is measurable. Then f−1({−∞}) ∈ M and f−1({∞}) ∈ M, because {−∞} and {∞} are Borel sets. If B ⊆ R is Borel then f−1(B) ∈M, and hence f−1(B) ∩ Y ∈M (since R is also Borel). Thus f is(More)
3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be(More)
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