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The Borel Functions Lecture Notes for Functional Analysis November 1, 2025 Kate Okikiolu Computer Support by Hans Lindblad Computer Apps: WinEdt, Adobe Acrobat Acknowledgements: Cambridge University 1983 { 1987. We are interested in the Borel functions on the real line in order to prove the spectral theorem for self-adjoint operators on a Hilbert space. However, what we want to discuss here is the nature of those functions which are the pointwise limits of the continuous func