Abstract

In recent years part of the literature on probabilistic causality concerned notions stemming from Reichenbach’s idea of explaining correlations between not directly causally related events by referring to their common causes. A few related notions have been introduced, e.g. that of a “common cause system” (Hofer-Szabó and Rédei in Int J Theor Phys 43(7/8):1819–1826, 2004) and “causal (N-)closedness” of probability spaces (Gyenis and Rédei in Found Phys 34(9):1284–1303, 2004; Hofer-Szabó and Rédei in Found Phys 36(5):745–756, 2006). In this paper we introduce a new and natural notion similar to causal closedness and prove a number of theorems which can be seen as extensions of earlier results from the literature. Most notably we prove that a finite probability space is causally closed in our sense iff its measure is uniform. We also present a generalisation of this result to a class of non-classical probability spaces