I am new to Riemann-Stieltjes integral. I want to ask a very basic question regarding changing the order of integration.
Let $ t > 0 $ and I have an integral that looks like this $$ \int_\mathbb{R} \int_0^t f(g(x)) dx dg(x). $$
What is the condition so that I change the order of integration? Or mathematically we could write the integral like this $$ \int_\mathbb{R} \int_0^t f(g(x)) dx dg(x) = \int_0^t \int_\mathbb{R} f(g(x))dg(x)dx $$