@Article{Alpay2024,
author = "Alpay, Daniel and Jorgensen, Palle",
title = "Finitely additive functions in measure theory and applications",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "3",
pages = "323--339",
doi = "https://doi.org/10.7494/OpMath.2024.44.3.323",
url = "https://doi.org/10.7494/OpMath.2024.44.3.323",
abstract = "In this paper, 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 \(\mu\)-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures \(\mu\), and to adjoints of composition operators.",
keywords = "Hilbert space, reproducing kernels, probability space, Gaussian fields, transforms, covariance, Itô integration, Itô calculus, generalized Brownian motion",
issn = "1232-9274"
}