Answer by Siminore for Is my counter-example correct?
If $1<p<+\infty$, the statement is true. This is rather standard, see for instance Lemma 4.8 in Kavian, Introduction à la théorie des points critiques, Springer-Verlag. You example assumes...
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In my homework for real-analysis I was asked to prove the following statement:On $[0,1]$, for $1\leq{}p<\infty$, If $f_{n}\rightarrow{}f$ a.e. and $||f_{n}||_{p}\leq{}M \space\space\forall\space...
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