# Question: Let f a b be an increasing function

Let f: [a, b] be an increasing function. Show that {x: f is discontinuous at x} is a set of measure 0.

## Answer to relevant Questions

a. Show that the set of all rectangles [a1, b1] x . x [an, bn] where each ai and each bi are rational can be arranged into a sequence (i.e. form a countable set). b. If A C Rn is any set and O is an open cover of A, show ...If f: A→R is non-negative and ∫ Af = 0, show that B = {x: f (x) ≠ 0} has measure 0.Let f: [a, b] → R be integrable and non-negative, and let Af = {(x, y): a < x < b and 0 < x < f (x)}. Show that Af is Jordan measurable and has area ∫ ba f.a. Let g: Rn → Rn be a linear transformation of one of the following types:Prove that a k-dimensional (vector) subspace of Rn is a k-dimensional manifold.Post your question