theorem Th4: :: CONVFUN1:4

for X being non empty RLSStruct
for f being Function of the carrier of X,ExtREAL st ( for x being VECTOR of X holds f . x <> -infty ) holds
( f is convex iff for x1, x2 being VECTOR of X
for p being Real st 0 < p & p < 1 holds
f . ((p * x1) + ((1 - p) * x2)) <= (p * (f . x1)) + ((1 - p) * (f . x2)) )