In Hou  it was shown that the class of approachable sets in a two-person game depended only on the mean vectors of the distributions involved subject to certain moment conditions. In this note we show that this result is, in fact, true whenever the mean vectors exist.
Harold Sackrowitz. "A Note on Approachability in a Two-person Game." Ann. Math. Statist. 43 (3) 1017 - 1019, June, 1972. https://doi.org/10.1214/aoms/1177692567