In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if
This theorem was announced by Czesław Ryll-Nardzewski. Later Namioka and Asplund gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.
Applications
The Ryll-Nardzewski theorem yields the existence of a Haar measure on compact groups.