Integration I: Multivariable Riemann Integral and Basic Ideas Toward the Lebesgue Integral

Igor Kriz and Aleš Pultr
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Igor Kriz: University of Michigan, Department of Mathematics
Aleš Pultr: Charles University, Department of Applied Mathematics (KAM) Faculty of Mathematics and Physics

Chapter 4 in Introduction to Mathematical Analysis, 2013, pp 97-116 from Springer

Abstract: Abstract In the first part of this chapter we will present a simple generalization of the one-dimensional Riemann integral which the reader already knows (see Section 8 of Chapter 1). To start with, we will consider the integral only for functions defined on n-dimensional intervals ( = “bricks”) and we will be concerned, basically, with continuous functions. Later, the domains and functions to be integrated on will become much more general.

Date: 2013
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DOI: 10.1007/978-3-0348-0636-7_4

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