Discrepancy has no relation to Monte Carlo?

Fallacy 4   If you use regular Monte Carlo, discrepancy doesn't have anything to do with it.

Counter Statement 4   The error bound on use of Monte Carlo is in terms of the Star Discrepancy of the random set of points generated by monte carlo. It doesn't matter how the points are generated, their Star Discrepancy determines the error bound.

However, if the function does not have finite variation, then the Koksma-Hlawka Inequality doesn't apply.