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Mathematical Analysis Fundamentals by Agamirza Bashirov

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image (11.33)

converges uniformly for y[c,d]image, then φC(c,d)image.

Proof

Consider, for example, the case I=[a,)image. Then

φ(y)=limbabf(x,y)dx,

image

where the limit is uniform for y[c,d]. By Theorem 9.34, for every b>a,abf(x,y)dx is a continuous function of ...

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