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Ryll-Nardzewski fixed-point theorem
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Ryll-Nardzewski fixed-point theorem : ウィキペディア英語版
Ryll-Nardzewski fixed-point theorem
In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if E is a normed vector space and K is a nonempty convex subset of E which is compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of K has at least one fixed point. (Here, a ''fixed point'' of a set of maps is a point that is fixed by each map in the set.)
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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