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Is it true that $$F(t) = \int_{K}f(x,t)dx$$ is continuous if $f$ is continuous and $K$ is compact? How to prove this?

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1 Answer 1

up vote 4 down vote accepted

If $f$ is continuous on $K$ compact, then it is dominated by a constant. Then you can use a very famous theorem involving integrals and dominated functions.

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