 So any agent that violates the Humean thesis must either fail to satisfy the AGM postulates, or the high-probability requirement. Note that the converse is not true: it is not the case that that if all pairs \(\langle \Bel_E, \Pr_E \rangle\) satisfy the Humean thesis, then \(\Bel_{{\bf A}^{\Pr}}\) must satisfy the AGM postulates. To prove this, suppose that \(\langle \Bel, \Pr \rangle\) satisfy the Humean thesis and \(\cap \Bel \subset E\) for some \(E\in{\bf A}^{\Pr}.\) If we let \(\Bel_E = \{E\}\), then \(\langle \Bel_E, \Pr_E \rangle\) satisfy the Humean thesis. However, such an agent patently violates rational and even Cautious Monotony. For a somewhat more detailed treatment of the relationship between AGM theory and the Humean thesis, see Section 6.3 in Genin (2019). For a full treatment, see Leitgeb (2017).