# Question: Let C C 0 1 x 0 1 be the union

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".

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Show by induction on n that R = [a1, b1] x..x [an, bn] is not a set of measure 0 (or content 0) if ai < bi for each i.If A = [a1, b1] x . x [an, bn] and f: A → R is continuous, define f: A → R byUse Theorem 3-14 to prove Theorem 3-13 without the assumption that g1 (x) ≠ 0.Let Kn = {xЄRn: x1 = 0 and x2. . . x n−1 > 0}. If MCKn is a k-dimensional manifold and N is obtained by revolving M around the axis x1 = . = xn-1=0, show that N is a (k + 1) -dimensional manifold. Example: the ...Let g: A →Rp be as in Theorem 5-1. If f: Rn → R is differentiable and the maximum (or minimum) of f on g-1 (0) occurs at , show that there are , such thatPost your question