  We discuss general notions of metrics and of Finsler structures which we call
weak metrics and weak Finsler structures. Any convex domain carries a canonical
weak Finsler structure, which we call its tautological weak Finsler structure.
We compute distances in the tautological weak Finsler structure of a domain and
we show that these are given by the so-called Funk weak metric. We conclude the
paper with a discussion of geodesics, of metric balls and of convexity
properties of the Funk weak metric.
