Zb. Hu et Bl. Lin, STRONGLY EXPOSED POINTS IN LEBESGUE-BOCHNER FUNCTION-SPACES, Proceedings of the American Mathematical Society, 120(4), 1994, pp. 1159-1165
It is a result of Peter Greim that if f is a strongly exposed Point of
the unit ball of Lebesgue-Bochner function space L(p)(mu , X) , 1 < p
< infinity, then f is a unit vector and f(t)/\\f(t)\\ is a strongly e
xposed point of the unit ball of X for almost all t in the support of
f . We prove that the converse is also true.