On the strong solutions of stochastic differential equations with nonsmooth coefficients

By means of purely probabilistic methods we prove the existence of strong solution of a stochastic differential equation
$$ dx(t,\omega)=f(x(t,\omega))\,dt+dw(t,\omega),x(0,\omega)=x_0\in R^1,\ 0\le t\le T<\infty, $$
in the case when the drift coefficient $f(x)$ is bounded and piecewise smooth or continuous function.