f-is-a-continue-and-positive-function-on-a-b-with-a-lt-b-let-m-max-x-a-b-f-x-prove-that-lim-n-1-b-a-a-b-f-n-x-dx-1-n-

Question Number 33167 by abdo imad last updated on 11/Apr/18

f i s a c o n t i n u e a n d p o s i t i v e f u n c t i o n o n [a, b] w i t h a < b

l e t m = {m a x}_{x \in [a, b]} f (x) p r o v e t h a t

{l i m}_{n \to \infty} {(\frac{1}{b - a} \int_{a}^{b} f^{n} (x) d x)}^{\frac{1}{n}}

Commented by abdo imad last updated on 12/Apr/18

p r o v e t h a t m = {l i m}_{n \to \infty} {(\frac{1}{b - a} \int_{a}^{b} f^{n} (x) d x)}^{\frac{1}{n}} .