Homework For Page 28
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# 3. We need to establish the def for a Lipschitz function:

     |(fg)(x) - (fg)(y)| \leq M |x - y| for all x, y in C.

     Start from the left hand side and inside the modulus add and
     subtract f(x)g(y). Then, with the use of the triangle inequality
     and the fact that f and g are uniformly bounded and Lipschitz
     you can finish off the problem.
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