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Random Variable

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## Homework Statement

Under what conditions does [itex] \lim_{s \to 0^{+}} \int_{0}^{\infty} f(x) e^{-sx} \ dx = \int_{0}^{\infty} f(x) \ dx [/itex] ?

## Homework Equations

## The Attempt at a Solution

If justification is ever offered, it's that [itex] \int_{0}^{\infty} f(x) \ dx [/itex] converges. But I'm not certain that's enough justification. It was suggested to me to also show that [itex] \int_{0}^{\infty} f(x) e^{-sx} \ dx [/itex] converges absolutely.