The results are related with numerical integration of functions in a reproducing kernel Hilbert space (RKHS). The authors define a notion of uniform distribution and discrepancy of sequences in an abstract set \(E\) in terms of a RKHS of functions on \(E\). In the case of the finite-dimensional unit cube the discrepancies introduced are closely related to the worst case error for numerical integration in a RKHS. The authors demonstrate that in the compact case the discrepancy tends to zero if and only if the the sequence is uniformly distributes in a certain sense. They also give a proof of an existence theorem for sequences uniformly distributed in the sense they defined. A consideration of the relation between the introduced notion of uniform distribution and the usual one is also given. Some examples are given.