On Hilbert extensions of Weierstrass' theorem with weights
In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm , where is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.
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