theorem :: RFUNCT_4:18

for f being PartFunc of REAL,REAL st f is total & ( for n being Element of NAT
for P, E, F being Element of n -tuples_on REAL st Sum P = 1 & ( for i being Element of NAT st i in dom P holds
( P . i >= 0 & F . i = f . (E . i) ) ) holds
f . (Sum (mlt (P,E))) <= Sum (mlt (P,F)) ) holds
f is_convex_on REAL