On the Causality and K-Causality between Measures
Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
Copernicus Center for Interdisciplinary Studies, ul. Szczepańska 1/5, 31-011 Kraków, Poland
Academic Editors: Mariusz P. Dąbrowski, Manuel Krämer and Vincenzo Salzano
Received: 31 January 2017 / Revised: 1 March 2017 / Accepted: 11 March 2017 / Published: 20 March 2017
Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation
onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “measure-theoretic” analogue of the characterization of
in terms of time functions.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Miller, T. On the Causality and K-Causality between Measures. Universe 2017, 3, 27.
Miller T. On the Causality and K-Causality between Measures. Universe. 2017; 3(1):27.
Miller, Tomasz. 2017. "On the Causality and K-Causality between Measures." Universe 3, no. 1: 27.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.