Before going through stochastic differential equations we need to understand how stochastic integrals work and their meaning inside the equation (SDE). The book I'm following is developing a construction of this integral using an analogous version to Riemann Sums. My question is, given a stochastic process $\{W_t; t \in [0, + \infty)\}$ where $W_t:\Omega \rightarrow \mathbb{R}$ and $$ \int_0^TW dW $$
how should I interpret $dW$? Is it the measure generated by the process? If so, how is described the measure generated by a process in general? Could I construct an analogous version of the Riemann sum but instead of considering the measure $dx$, considering $dW$ and integrate any other stochastic process with respect to this measure? How is interpreted the integral of a stochastic process in general? Does normal integration not apply in such cases, even if we fix $w\in \Omega$?
Many thanks in advance.