Finitely additive functions in measure theory and applications
Probability
2022-05-17 v1
Abstract
We consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of -Brownian motion, to stochastic calculus via generalized It\^o-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures , and to adjoints of composition operators.
Cite
@article{arxiv.2205.07462,
title = {Finitely additive functions in measure theory and applications},
author = {Daniel Alpay and Palle Jorgensen},
journal= {arXiv preprint arXiv:2205.07462},
year = {2022}
}