75 research outputs found
Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions
Given a strictly increasing, continuous function ,
based on the cost functional , we
define the -Wasserstein distance between
probability measures on some metric space . The function
will be assumed to admit a representation
as a composition of a convex and a concave function and , resp.
Besides convex functions and concave functions this includes all
functions.
For such functions we extend the concept of Orlicz spaces,
defining the metric space of measurable functions such that, for instance,
d_\vartheta(f,g)\le1\quad\Longleftrightarrow\quad
\int_X\vartheta(|f(x)-g(x)|)\,d\mu(x)\le1.$
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