Question, Am I right about what I state down here:
I want to find the Laplace transform, of an integral:
$$\int_0^\infty e^{-\text{s}t}\left\{\int_0^\infty\text{y}\left(t,\text{x}\right)\space\text{d}\text{x}\right\}\space\text{d}t$$
So, in general I am studying the double integral:
$$\mathcal{I}\left(\text{s}\right)=\int_0^\infty\text{f}\left(\text{s},t\right)\left\{\int_0^\infty\text{y}\left(t,\text{x}\right)\space\text{d}\text{x}\right\}\space\text{d}t=\int_0^\infty\int_0^\infty\text{f}\left(\text{s},t\right)\text{y}\left(t,\text{x}\right)\space\text{d}\text{x}\space\text{d}t$$
In order to switch the order of integration, we can apply Fubini's theorem:
$$\color{red}{\mathcal{I}\left(\text{s}\right)=\int_0^\infty\int_0^\infty\text{f}\left(\text{s},t\right)\text{y}\left(t,\text{x}\right)\space\text{d}t\space\text{d}\text{x}}$$
The red part is equal when:
$$\int_0^\infty\int_0^\infty\left|\text{f}\left(\text{s},t\right)\text{y}\left(t,\text{x}\right)\right|\space\text{d}\text{x}\space\text{d}t\space<\text{n}\to\infty$$
But when I look at [this website][1], they only talk about when the integral equals a definite value, and my integral contains the variable $\text{s}$, how do I deal with that?