Measure and Integral
This accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them.
This material in Measure and Integral: Theory and Practice is typically covered in a graduate course and is almost always treated in an abstract way, with little or no motivation. The author employs a plethora of examples and exercises and strives to motivate every concept with its historical background. This textbook is accessible to a wider range of students, including at the undergraduate level.
A major problem facing anyone teaching measure theory is how to combine the elementary approach (measure on the real line or in the plane) and the abstract measure theory. The author develops a theory of measure in the plane, then shows how to generalize these ideas to an abstract setting.
The result is a textbook accessible to a wider range of students.
The material requires a good understanding of topics often referred to as advanced calculus, such as Riemann integration on Euclidean spaces and series of functions. Also, a reader is expected to be proficient in the basics of set theory and point-set topology, preferably including metric spaces.
John Srdjan Petrovic was born in Belgrade, Yugoslavia. He earned his PhD from the University of Michigan under the direction of Dr.Carl Pearcy. His research area is the theory of operators on Hilbert space, and he has published more than 30 articles in prestigious journals. He is a professor of mathematics at Western Michigan University and his visiting positions include Texas A&M University, Indiana University, and University of North Carolina Charlotte. His text, Advanced Caluclus: Theory and Practice, is in its second edition (CRC Press).