I'm reading the stochastic process by myself, and I have some confusion about ito integral. Based on what I know: the quadratic variance of brownian motion $W(t)$ (for a single $\omega$) converges to $t$ in the $L^2 norm$ sense, which can be written:
$$\int_\Omega \bigg(\big(W(T)-W(0)\big)^2-T\bigg)^2d\mathbb P(\omega)\to0$$
But how does this relate to that we can substitute $dWdW$ with $dt$ in the Riemann integral? Is there any material that I can read to fill the gap? thanks!