Calculus of variations
Henceψis convex. on the real line. AsxsatisÖes the Euler-Lagrangeequationψ^0 ( (^0) )=0 and asψis convexψhas a minimum atλ= 0 ,so
Ψ(x)=ψ( 0 )ψ( 1 )=Ψ(y)
for everyy,which proves the theorem.
greg delong
(Greg DeLong)
#1
Henceψis convex. on the real line. AsxsatisÖes the Euler-Lagrangeequationψ^0 ( (^0) )=0 and asψis convexψhas a minimum atλ= 0 ,so
Ψ(x)=ψ( 0 )ψ( 1 )=Ψ(y)
for everyy,which proves the theorem.