Ito Integral
- Consider a set of stochastic process $f(t)$ mainly such that
a) $ E\left(\int_0^{+\infty}f(t)^2 \,dt\right) < \infty. $
Denote this set of stochastic process as $M^2$.
Question:
a) For each $w$, $f(t,$w$)$ is a continuous function, so we all know a bounded continuous function will be Riemann integrable, but why it is square integrable too, i.e. why $ \int_0^{\infty}f(t)^2 \,dt $ has to exist
i.e. why the set $ M^2 $ will for sure be in $ L^2 $ when integrating over time $t$ on the time line $(0, \infty)$?
Thank you