Yes. The effect of having a coarser partition around a mesh point is countered by the effect of a higher frequency of hitting that partition. This actually is t

Yes. The effect of having a coarser partition around a mesh point is countered by the effect of a higher frequency of hitting that partition. This actually is the essence of importance sampling. For the purposes of numerical integration, as long as the integrand is relatively smooth with respect to the partition size, there shouldn't raise any serious problem. On the contrary, if the integrand does vary wildly between two adjacent floating point numbers, then the real issue here is that the precision (single, double, quadruple, etc.) used is not fine enough, rather than the deviation from uniform distribution.