Ryll-Nardzewski fixed-point theorem

<h2 id="applications">Applications</h2>
<p>The Ryll-Nardzewski theorem yields the existence of a <a href="/facts/Haar_measure/2IcmTcuU">Haar measure</a> on compact groups.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
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<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Fixed-point_theorem/Jvkz4SUu">Fixed-point theorems</a></li>
<li><a href="/facts/Fixed-point_theorems_in_infinite-dimensional_spaces/4rJmoRml">Fixed-point theorems in infinite-dimensional spaces</a></li>
<li><a href="/facts/Markov-Kakutani_fixed-point_theorem/wAha0RPr">Markov-Kakutani fixed-point theorem</a> - abelian semigroup of continuous affine self-maps on compact convex set in a topological vector space has a fixed point</li></ul>

<ul><li>Andrzej Granas and <a href="/facts/James_Dugundji/xCy4DgGy">James Dugundji</a>, <i>Fixed Point Theory</i> (2003) Springer-Verlag, New York, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-00173-5.</li>
<li><a href="http://www.math.harvard.edu/~lurie/261ynotes/lecture26.pdf">A proof written by J. Lurie</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Ryll-Nardzewski, C. (1962). "Generalized random ergodic theorems and weakly almost periodic functions". Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 10: 271–275. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Namioka, I.; Asplund, E. (1967). "A geometric proof of Ryll-Nardzewski's fixed point theorem". Bull. Amer. Math. Soc. 73 (3): 443–445. doi:10.1090/S0002-9904-1967-11779-8. <a href="/wiki/Isaac_Namioka" target="_blank">/wiki/Isaac_Namioka</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Ryll-Nardzewski, C. (1967). "On fixed points of semi-groups of endomorphisms of linear spaces". Proc. 5th Berkeley Symp. Probab. Math. Stat. 2: 1. Univ. California Press: 55–61. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Bourbaki, N. (1981). Espaces vectoriels topologiques. Chapitres 1 à 5. Éléments de mathématique. (New ed.). Paris: Masson. ISBN 2-225-68410-3. <a href="2-225-68410-3" target="_blank">2-225-68410-3</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
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Ryll-Nardzewski fixed-point theorem open-in-new

Ryll-Nardzewski fixed-point theorem