  Niederreiter [H.Niederreiter, Error bounds for quasi-Monte Carlo integration
with uniform point sets, Journal of computational and applied mathematics 150
(2003), 283-292] established new bounds for quasi-Monte Carlo integration for
nodes sets with a special kind of uniformity property. Let (X,\mathscr{A},\mu)
be an arbitrary probability space, i.e., X is an arbitrary nonempty set,
\mathscr{A} a \sigma-algebra of subsets of X, and \mu a probability measure
defined on \mathscr{A}. The functions considered in Niederreiter's paper are
bounded \mu-integrable functions on X. In this note, we extend some of his
results for bounded \mu-integrable functions to essentially bounded
\mathscr{A}-measurable functions. So Niederreiter's bounds can be used in a
more general setting.
