Let {S,}EN is a disjoint seqeuence of measurable sets , then: US, µ(S,)

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A: This is a problem of Real topology, metric topology.

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Q: rcise: Prove that every finite set S of R" has no accumulation point.

A: Proof of the the given theorem is given as

Q: 4. Show that if A is closed in Y and Y is closed in X, then A is closed in X. Verify it and make…

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Q: (ii). Prove that a set SCRis everywhere dense iff it intersects every non-empty open sets in R.Prove…

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Q: Show that Let ECR" is measurable set. If µ(E) >0, then E have a non-measurable subset

A: Here, we introduce the notation Gr :=G∩[0, r) + 1-r ∪ G∩[r,1) - r for G⊂[0,1) and r∈R. Note that…

Q: Let {S,},EN is a disjoint seqeuence of measurable sets , then: HUS,

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Q: a. Show that the null-space N(A) is a convex set. Is it true for every A?

A: As both questions are of different type,we shall solve first Que only. For other questions kindly…

Q: let to be anonempty subset of abounded set E-Show that infESinf to Ssup E ssup E

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Q: let A Set bounded below, ילC erove that C. nf A inf C A %3D

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A: Here, the given set is X=a,b,c and collection is X,∅,a,a,b,c.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.