2. Let E be closed and bounded in Rn and let g, fk,gk : E -+ R...

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2. Let E be closed and bounded in Rn and let g, fk,gk : E -+ R be continuous 287 on E with gk 2: 0 and h 2: h··· 2: Ik 2: 0 for kEN. If 9 = 2:~1 gk converges pointwise on E, prove that 2:%"=1 Ikgk converges uniformly on E.

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