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Universe 2017, 3(1), 27;

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
(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)
View Full-Text   |   Download PDF [257 KB, uploaded 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 K + 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 K + in terms of time functions. View Full-Text
Keywords: causal relations; Lorentzian optimal transport theory; time functions causal relations; Lorentzian optimal transport theory; 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).

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Miller, T. On the Causality and K-Causality between Measures. Universe 2017, 3, 27.

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