Uniqueness of disintegration: Addendum to “Stabilities of shape identification inverse problems in a Bayesian framework” [J. Math. Anal. Appl. 486 (2) (2020) 123903]

The strong uniqueness of disintegration holds if the σ-algebra on the considered space is countably generated. This strong uniqueness yields the strong uniqueness of the posterior as a disintegrating measure in the Bayesian inverse problem discussed in [4].