On uniform distribution of sequences inGF {q, x } and [GFq, x]

Analogs are proved for sequences in Φ=GF[q, x] and Φ′=GF {q, x } of results proved in 1962 by C.L. Vanden Eynden concerning uuiform distribution of sequence of integers related to sequences of real numbers. The concept of uniform distribution (mod m), m an integer, in Vanden Eynden's work is sometimes replaced here by modified forms of uniform distribution (mod M) M ∈ Φ.