  In [K.J. Ciosmak, Applications of Strassen's theorem and Choquet theory to
optimal transport problems, to uniformly convex functions and to uniformly
smooth functions, Nonlinear Anal. 232 (2023), Paper No. 113267, 32 pp.],
Theorem 2.3. does not suffice for its applications. We strengthen Theorem 2.1.
and Theorem 2.3., so that they imply their claimed consequences. Moreover, we
correct a minor flaw in the proof of Proposition 2.4..
