It's time for some learning! By "Problem of the Day", I mean an occasional problem when I feel like posting. Suggestions are welcome.

(Real Analysis) Show that

where C[a,b] is the space of continuous functions from [a,b] to the reals. Or, slightly more generally, show that for any f in L^\infty, the limit of the L^p norms of $f$ as p tends to infinity is the L^\infty norm of f.