Prerequisites
Required background:
Measure theory in $\mathbb{R}^n$ (Lebesgue integral, measurable sets, convergence theorems, covering lemmas, Lebesgue differentiation), basics of functional analysis (metric spaces, Hilbert and Banach spaces, duality, boundedness, Riesz representation, Banach-Alaoglu theorem).Bonus / Helpful to know:
Familiarity with any bit of the following should help: basics of partial differential equations (particularly elliptic and Hamilton-Jacobi equations), stochastic processes, convex optimization, numerical linear algebra, the calculus of variations, differential geometry.