On the Stochastic Burgers Equation and the Axiom of Choice

Details On the Stochastic Burgers Equation and the Axiom of Choice On the Stochastic Burgers Equation and the Axiom of Choice

2010-07-13

arxiv.org/abs/1007.2375v1

Mathematics

General Mathematics

56 pages

Scientific paper

The equivalence of the Choice Axiom and Tychonov compactness was proved by Kelley in 1950. Tychonov compactness is required to prove existence of the minimiser of an action functional under standard hypotheses. Solutions to the inviscid Burgers equation may be constructed by considering the minimising trajectories of associated action functionals. This construction has been used in the literature to construct an invariant measure for the stochastic inviscid Burgers equation. This article compares results that may be obtained with and without using this representation and draws conclusions about the Choice Axiom.

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