7. If f = L::;;O=l!k converges uniformly on a set E ~ R and if gl is

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7. If f = L::;;O=l!k converges uniformly on a set E ~ R and if gl is bounded on E with gk(X) ~ gk+1(X) ~ 0 for all x E E and kEN, prove that L::;;O=l fkgk converges uniformly on E.

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