I just start to learn Riemann-Stieltjes integral. But I feel confused about what is $g(x)$ for in Riemann-Stieltjes integral.
Here is the definition of Riemann-Stieltjes integral.
My understanding is that in integral, we want a partition of the domain of the function, $f(x)$, in this case.
In this sense, we already have a partition P. So what is $g(x) $for?
To choose a proper partition from all possible partitions?
And why $g(x) $ needs to be an increasing real-valued function also defined in $[a,b]$?