# Question: Let U be the open set of Problem 3 11

Let U be the open set of Problem 3-11. Show that if f = X except on a set of measure 0, then f is not integrable on [0, 1]

## Relevant Questions

14. If is a closed rectangle, show that is Jordan measurable if and only if for every there is a partition of such that , where consists of all subrectangles intersecting and consists of allsubrectangles contained ...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.Let g1, g2: R2 → R be continuously differentiable and suppose D1 g2= D2 R1.. As in Problem 2-21, let(a) Let A C Rn be an open set such that boundary A is an (n - 1) -dimensional manifold. Show that N = AU boundary A is an -dimensional manifold with boundary. (It is well to bear in mind the following example: if A = {x ...a. If f is a differentiable vector field on M C Rn, show that there is an open set AЭM and a differentiable vector field F on A with F(x) = F (x) for xЄM. b. If M is closed, show that we can choose A = Rn.Post your question