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Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

3 votes

Approximation with continuous functions

All the answers here rely on measure-theoretic ideas to give a negative answer. I feel that this does not exactly meet the point, instead I would say: You did not quite ask the right question, but if …
Matthias Ludewig's user avatar