So for my LA class I am to prove that all functions f such that they are contiunous over the [0,1] and their integral over the same integral = 0 is a subspace of the function space of continuous functions over [0,1]. So I think my proof is fine but I have one semi-technical question. Is it ok just to state:(adsbygoogle = window.adsbygoogle || []).push({});

"if f, g are continuous over [0,1] f+g must also be by a theorem of calculus and if f is continuous rf must also be by a theorem of calculus."

I'm leaning towards no but I'm not sure

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# Function Space question:

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