Unformatted text preview: false. (a) An equicontinuous, pointwise bounded subset of C [ a,b ] is compact. (b) The function χ Q is Riemann integrable on [0 , 1]. (c) The function χ Δ is Riemann integrable on [0 , 1], where Δ denotes the Cantor middlethird set. (We have already run into this set in Homework 2, Problem 5). (d) T α {R α [ a,b ] : α increasing } = C [ a,b ]. (e) If f is a monotone function and α is both continuous and nondecreasing, then f ∈ R α [ a,b ]. (f) There exists a nondecreasing function α : [ a,b ] → R and a function f ∈ R α [ a,b ] such that f and α share a commonsided discontinuity. (g) If f ∈ R α [ a,b ] with m ≤ f ≤ M and if ϕ is continuous on [ m,M ], then ϕ ◦ f ∈ R α [ a,b ]. 1...
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 Spring '14
 Math, Continuous function, Order theory, Riemann integral, rα

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