Till now, i have learned abstract Integration, all basic properties of the (n-dimensional) Lebesgue(-Stieltjes) measure and the lebesgue integral is an extension of Riemann integral.

Here's an illustration i'm curious about:

Let $\Gamma$ be a complex-valued gamma function.

Often, it's written in texts $\Gamma(z)=\int\_{0}^\infty t^{z-1}e^{-t} dt$. ($Re(z)>0$)

If i understand this integral as the Lebesgue-integral, it makes sense to me. However if this integral is the Riemann-integral, i wonder which limit should be taken first. That is, is it taking limit first to $0$ and then to $\infty$? Or first to $\infty$ then to $0$? Or an order of taking limit doesn't matter? What are relations between the Lebesgue integral and Riemann *improper* integral?

Please suggest me a text which could answer these questions. However, i don't want to spend *very much* time on this. I hope i can learn these topics within 2 or 3 days. Thank you :)