On Koksma-Hlawka inequality
  The classical Koksma Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma Hlawka type inequality which applies to piecewise smooth functions $f\chi_{\Omega}$, with $f$ smooth and $\Omega $ a Borel subset of $[0,1]^{d}$. 
L. Brandolini, L. Colzani, G. Gigante and G. Travaglini
math.FA