A measure space (X, μ) is said to be separable if there is a countable family of measurable subsets {E}_1 so that if E is any measurable set of finite measure, then μ(ΕΔΕn) → 0 as k → ∞, for an appropriate sequence {n} which depends upon E. Here AAB denotes the symmetric difference of the sets A and B, that is, AAB = (A − B) U (B − A). (a) Prove that Rd is separable. (b) The space LP = LP(X, ) is separable if there exists a countable collection

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A: given that (1) (a)                                    S=n(-1)n:n∈N=2k(-1)2k:n=2k,…

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Q: 1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and…

A: a) The given set is,S=n-1n:n∈ℕ

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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