Well... I have a problem with Ito integral $\int_{a}^{b} x(t)dw(t)$, where x(t) is a stochasic process, and w(t) is Brownian motion (or Wiener process ). It is said that Ito integral cannot be considered as a Riemann-Stjelties integral because dW has no bounded variation. So for example let us consider sequence of approximating sums $\sum _{i=1} ^{n} (x(t') w(t_{i} - t_{i-1}))$ where $t' \in [t_{i-1}, t_{i}]$ and $a=t_{0}<... is a division of integral [a,b]. In this case value of this integral does depend of choise of t'! And I've read that this is because Wiener process has no bounded variation.