We discuss the reconciliation problem between probability measures: given n⩾2 probability spaces
$(\Omega,{\mathcal{F}}_1,{\mathbb{P}}_1),\ldots,(\Omega,{\mathcal{F}}_n,{\mathbb{P}}_n)$
with a common sample space, does there exist an overall probability measure
${\mathbb{P}} \ \text{on} \ {\mathcal{F}} = \sigma({\mathcal{F}}_1,\ldots,{\mathcal{F}}_n)$
such that, for all i, the restriction of
${\mathbb{P}} \ \text{to} \ {\mathcal{F}}_i$
coincides with
${\mathbb{P}}_i$
? General criteria for the existence of a reconciliation are stated, along with some counterexamples that highlight some delicate issues. Connections to earlier (recent and far less recent) work are discussed, and elementary self-contained proofs for the various results are given.