  We consider finite state non-deterministic but unambiguous transducers with
infinite inputs and infinite outputs, and we consider the property of Borel
normality of sequences of symbols. When these transducers are strongly
connected, and when the input is a Borel normal sequence, the output is a
sequence in which every block has a frequency given by a weighted automaton
over the rationals. We provide an algorithm that decides in cubic time whether
a unambiguous transducer preserves normality.
