Transcription of Theory of functions of a real variable.
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Theory of functions of a real variable.
Theory of functions of a real SternbergMay 10, have taught the beginning graduate course in real variables and functionalanalysis three times in the last five years, and this book is the result. Thecourse assumes that the student has seen the basics of real variable Theory andpoint set topology. The elements of the topology of metrics spaces are presented(in the nature of a rapid review) in Chapter course itself consists of two parts: 1) measure Theory and integration,and 2) Hilbert space Theory , especially the spectral theorem and its Chapter II I do the basics of Hilbert space Theory , what I can dowithout measure Theory or the Lebesgue integral. The hero here (and perhapsfor the first half of the course) is the Riesz representation theorem. Includedis the spectral theorem for compact self-adjoint operators and applications ofthis theorem to elliptic partial differential equations.
In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for …
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