Brouwer fixed point theorem in L 0 d Report as inadecuate

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Fixed Point Theory and Applications

, 2013:301

First Online: 19 November 2013Received: 17 May 2013Accepted: 21 October 2013


The classical Brouwer fixed point theorem states that in R d every continuous function from a convex, compact set on itself has a fixed point. For an arbitrary probability space, let L 0 = L 0 Ω , A , P be the set of random variables. We consider L 0 d as an L 0 -module and show that local, sequentially continuous functions on L 0 -convex, closed and bounded subsets have a fixed point which is measurable by construction.

MSC: 47H10, 13C13, 46A19, 60H25.

Keywordsconditional simplex fixed points in L 0 d   Download fulltext PDF

Author: Samuel Drapeau - Martin Karliczek - Michael Kupper - Martin Streckfuß


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