Which is a linear functional in a Lp space?

Lp SPACES. A linear functional is bounded if and only if it is continuous. For Lp spaces, we will use the Radon-Nikodym theorem to show that Lp(X) may be identi ed with Lp0(X) for 1 <p<1. Under a ˙- niteness assumption, it is also true that L1(X) = L1(X), but in general L1(X) 6= L1(X).
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