When does this equality hold and how can I prove it:
$$\int_0^\infty\text{f}\left(\text{s},t\right)\left\{\int_0^\infty\text{y}\left(t,x\right)\space\text{d}x\right\}\space\text{d}t=\int_0^\infty\left\{\int_0^\infty\text{f}\left(\text{s},t\right)\text{y}\left(t,x\right)\space\text{d}t\right\}\space\text{d}x$$
Using Fubini's theorem, is this true when:
$$\int_0^\infty\int_0^\infty\left|\text{f}\left(\text{s},t\right)\text{y}\left(t,x\right)\right|\space\text{d}x\space\text{d}t\space<\text{n}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\text{when}\space\space\text{n}\to\infty$$
Am I true about that?