An analogue of a theorem of Szüsz for formal Laurent series over finite fields

About 40 years ago, Szüsz proved an extension of the well-known Gauss–Kuzmin theorem. This result played a crucial role in several subsequent papers (for instance, papers due to Szüsz, Philipp, and the author). In this note, we provide an analogue in the field of formal Laurent series and outline applications to the metric theory of continued fractions and to the metric theory of diophantine approximation.