Remark Definition Convergence In A Normed Space Let X Id Be A Normed Space A Sequence Fr In X Is Said To Conv 1 (14.04 KiB) Viewed 32 times
Remark Definition Convergence In A Normed Space Let X Id Be A Normed Space A Sequence Fr In X Is Said To Conv 2 (13.42 KiB) Viewed 32 times
Remark: Definition (Convergence in a normed space) Let (X, ||-ID be a normed space. A sequence {fr} in X is said to converge to an element f in X if given e > 0, there is N such that for all n > N we have || An - fl| <€. In the problems below LP stands for LP ([0,1])
1 Suppose that 1<p < and + = 1. Assume that {fn} is a sequence р 9 in LP such that fn(0) + f(x) almost everywhere and f e LP. Moreover, there is M >0 so that ||fr|| <M for all n. Show that for each ge L' we have so do limin =
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