Question: If f, g L[a, ], show that f g L[a,1]. Moreover, if ||h|| :a |h| for any h L[a,], show that

If f, g ∈ L[a, ∞], show that f ± g ∈ L[a,1]. Moreover, if ||h|| :∫∞a |h| for any h ∈ L[a,∞], show that ||f + g|| < ||f|| + ||g||.

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