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Arakelyan's theorem

 Home Mathematics Fields of mathematics Mathematical analysis Theorems in analysis Theorems in approximation theory
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Arakelyan's theorem is a result in approximation theory, particularly concerning the approximation of continuous functions by certain classes of functions. It states that if \( f \) is a continuous function defined on a compact subset of \( \mathbb{R}^n \) that is not identically zero, then there exists a sequence of functions that can approximate \( f \) arbitrarily closely.

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