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arXiv · 1801.05505

Time functions and $K$-causality between measures

Tomasz Miller
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Abstract

Employing the notion of a coupling between measures, drawn from the optimal transport theory, we study the extension of the Sorkin-Woolgar causal relation $K^+$ onto the space $\mathscr{P}(\mathcal{M})$ of Borel probability measures on a given spacetime $\mathcal{M}$. We show that Minguzzi's characterization of $K^+$ in terms of time functions possesses a "measure-theoretic" generalization. Moreover, we prove that the relation $K^+$ extended onto $\mathscr{P}(\mathcal{M})$ retains its property of antisymmetry for $\mathcal{M}$ stably causal.

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Tomasz Miller. 2018-01-16. Time functions and $K$-causality between measures. https://doi.org/10.1088/1742-6596/968/1/012008

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