# Question: a If C is a set of content 0

a. If C is a set of content 0, show that the boundary of C also has content 0.

b. Give an example of a bounded set C of measure 0 such that the boundary of C does not have measure 0.

b. Give an example of a bounded set C of measure 0 such that the boundary of C does not have measure 0.

**View Solution:**## Answer to relevant Questions

Let A be the set of Problem 1-18. If T = ∑i = 1 (bi − ai) Give an example of a bounded set C of measure 0 such that ∫ AXC does not exist.Let C C [0, 1] x [0, 1] be the union of all {p/q} x [0, 1] where p/q is a rational number in [0, 1] written in lowest terms. Use C to show that the word ``measure" in Problem 3-23 cannot be replaced with ``content".If f: [a, b] x [c, d] → R is continuous and D2f is continuous, define F (x, y) = ∫xa (t,y) dt a. Find D1F and D2F. (b) If G (x) = ∫ g(x) f (t, x) dt, find G1 (x).(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 ...Post your question