A mean value theorem for metric spaces. Issue 5 (21st January 2015) - Carvalho Neto, P. M.
Abstract : We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the ɛ ↦ δ ( ɛ ) relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure.