Let f, {fk} ∈ Lp(E), where E ⊂ Rⁿ is a measurable set. Show that if ||f - fk||p → 0, then ||fk||p → ||f||p. Conversely, if fk → f a.e. and ||fk||p → ||f||p, show that ||f - fk||p → 0.
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