Fourier Analysis and Measure Theory Question 1 Let (V;

Fourier Analysis and Measure Theory Question 1 Let (V; jj jj) be a complex and normed vector space. ALet (fn)1n=1 be a sequence in V . When is g 2 V called a sequential point of accumulation (or limit point) of (fn)1n=1. Give the denition. BShow that: if (fn)1n=1 is a sequence in V and g 2 V a sequential point of accumulation then the sequence (fn)1 n=1 is a subsequence which converges to g. Question 2 Let ?? be the semiring of all cells (a; b]; a b in R and let g : R ! R an increasing and right continuous function (i.e. limh#0 g(x + h) = g(x) for all x 2 R). For (a; b] 2 ?? we dene (a; b] = g(b) ?? g(a) AProve that is a measure. Question 3 Let X 6= ;;a -algebra in X and : ! [0;1] a measure. Assume that (X)