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Lp spaces

Suppose m is a positive measure on X,
m(X) < inf
f is an element of L^(inf),
||f||_inf<inf
and
a_n= int (|f|^n)dm for n = 1,2,...
where the integral is evaluated over the set X
Show that
lim as n->inf of (a_(n+1))/(a_n) is equal to ||f||_inf

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