1. The problem statement, all variables and given/known data Let f_n be a sequence of function whcih converges pointwise on [0,1] where each one is Lipschitz with the same constant C. Prove that the sequence converges uniformly. 2. Relevant equations A function is called Lipschitz with Lipschitz constant C if |f(x)-f(y)| <= C|x-y| for all x,y in its domain. Let f_n be a sequence of functions defined on a set S. f is the pointwise limit of f_n if for all t in S lim n to infinity f_n(t) = f(t) 3. The attempt at a solution I know that somehow I must show if for all epsilon > 0 there exists N in naturals such that sup|f_n(t) -f(t)| < epsilon if n>N for all t in [0,1] Or show the Uniform Cauchy Criterion holds : for all epsilon > 0 there exists N in naturals such that |f_n(t) -f_m(t)| < epsilon for all m,n > t for all t in [0,1].