Lipschitz

Def 17.3

is called Lipschitz
if
where is called Lipschtz constant

Thm pg.143

if is Lipschitz function, is uniformly continue in

Thm 24.1

The best(smallest) Lipschitz constant equal to the first order derivative of a differentiable function.

OH 35.1

Thm D

for continue, bounded and integrable Lipschitz

Proof

by FT:

Thm E

and is bounded is Lipschitz

Proof

by MVT

Thm

uniformly continue Lipschitz