Abstract
An important result in elementary analysis is Weierstrass’ theorem, asserting that on a bounded closed interval every continuous function can be approximated uniformly by polynomial functions. We prove an extension of this result. The theorem itself lies outside our sphere of interest, but it is crucial for the representation theorems in our later chapters.
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Groenewegen, G.L.M., van Rooij, A.C.M. (2016). The Stone-Weierstrass Theorem. In: Spaces of Continuous Functions. Atlantis Studies in Mathematics, vol 4. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-201-4_3
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DOI: https://doi.org/10.2991/978-94-6239-201-4_3
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-6239-200-7
Online ISBN: 978-94-6239-201-4
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