let be a Lebesgue integrable function on [0,1], and let be a sequence of bounded measurable functions on [0,1] that converges uniformly to a function . Prove that
help will be appreciated so much
i dont see why has to converge uniformly to . to me if , then (i am not sure how to show). and since there exists such that and since is integrable, so is .
by dominated convergence theorem, i think we get what we want.
can someone help me with this one?
So, can you prove that your sequence uniformly converges to if the sequence uniformly converges to ?