  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.
