A transfunction is a function which maps between sets of finite measures on
measurable spaces. In this paper we characterize transfunctions that correspond
to Markov operators and to transport plans. A single transfunction of this type
will contain the `instructions' common to several different Markov operators
and transport plans. We also define two kinds of adjoints to transfunctions.
The Markov adjoint of a transfunction from $X$ to $Y$ is a certain
transfunction from $Y$ to $X$. The Radon adjoint of a transfunction from $X$ to
$Y$ is a certain linear and bounded operator between Banach spaces of functions
on $Y$ and $X$. Both types of adjoints are defined via integral properies and
their existence implies strong $\sigma$-additivity of the transfunction.
@article{1810.08349,
author = {Bentley, Jason and Mikusi\'nski, Piotr},
title = {Markov Operators, Transport Plans and Transfunctions},
journal = {arXiv},
volume = {2018},
number = {0},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/1810.08349}
}
Bentley, Jason; Mikusiński, Piotr. Markov Operators, Transport Plans and Transfunctions. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.08349/