Let be $f\in C^0(\mathbb{R})$, such that $f\geq 0$.
I suppose that $\int_{\mathbb{R}}f(t) dt<+\infty$.
Under these hypothesis, can I say that
$\int_{0}^{+\infty} f(t)\; dt-\int_{-\infty}^{0} f(t)\;dt<+\infty$ ?
I think yes, since $\int_{\mathbb{R}}f(t) dt<+\infty$ iff $\int_{0}^{\infty}f(t)dt<+\infty$ e $\int_{-\infty}^{0}f(t)dt<+\infty$.
The viceversa is not true, right?
So my question is: If $a,b\geq 0$ and $a<+\infty$, $b<+\infty$, then $a-b<+\infty$?
Thank you for the clarification!