Zakon E. Mathematical Analysis II

West Lafayette: The Triillia Group, 2017. — 434 p. (corrected edition)This is a multipurpose text. When taken in full, including the “starred” sections, it is a graduate course covering differentiation on normed spaces and integration with respect to complex and vector-valued measures. The starred sections may be omitted without loss of continuity, however, for a junior or senior course. One also has the option of limiting all to En , or taking Riemann integration before Lebesgue theory (we call it the “limited approach”). The proofs and definitions are so chosen that they are as simple in the general case as in the more special cases. Our principle is to keep the exposition more general whenever the general case can be handled as simply as the special ones (the degree of the desired specialization is left to the instructor). Often this even simplifies matters - for example, by considering normed spaces instead of En only, one avoids cumbersome coordinate techniques. Doing so also makes the text more flexible.About the Author.
Differentiation on En and Other Normed Linear Spaces.
Volume and Measure.
Measurable Functions. Integration.
Calculus Using Lebesgue Theory.