Titlebook: Basic Real Analysis; Houshang H. Sohrab Textbook 20031st edition Birkhäuser Boston 2003 Arithmetic.Cardinal number.Counting.Equivalence.ca

Extemporize

Lebesgue Measure,erested in a larger class of functions containing simultaneously .. One of our goals in this chapter will be to introduce and study this class. Although we start with F. Riesz’s definition of a measurable function, we shall later give the more general definitions of ., ., . and prove the equivalence

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Textbook 20031st editioninto the main text, as well as at the end of each chapter .* Emphasis on monotone functions throughout .* Good development of integration theory .* Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis .* Solid preparation for deeper stud

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velopment of integration theory .* Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis .* Solid preparation for deeper stud978-1-4612-6503-0978-0-8176-8232-3

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MORPH

Sequences and Series of Real Numbers,n most cases, however, the proofs are given in appendices and omitted from the main body of the course. To give rigorous proofs of the basic theorems on convergence, continuity, and differentiability, one needs a precise definition of real numbers. One way to achieve this is to start with the . of r

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FACT

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GLEAN

RADE

Sequences and Series of Functions,asier to investigate. We have already done this on a few occasions. For example, in Chapter 4, we looked at the . approximation of continuous functions by step, piecewise linear, and polynomial functions. Also, in Chapter 7, we proved that each bounded continuous function on a closed bounded interva