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I'm reading a monograph that considers the following problem: $$\inf_{z(t) \in C^1} \int_0^1 c\bigg(\frac{dz(t)}{dt}\bigg) dt\\ z(0) = x, z(1) = y$$ Here $c$ is a convex function, $z(t)$ are paths ...

$\newcommand{\diff}{ \, \mathrm d}$ Let $X,Y$ be Polish spaces, $\mathcal C_b(X)$ the space of all real-valued bounded continuous functions on $X$, $\mathcal P(X)$ the space of Borel probability ...