Measure and Integration: First Steps
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This book introduces a beginning graduate student in Mathematics to the essentials of measure theory. This theory extends the notion of the length of an interval to more general notions of the size of a set. These ideas are then used to build abstract versions of integration theory. We discuss how to build many such measures, Lebesgue and Lebesgue-Stieljes Integration and include a lengthy treatment of classical Riemann and Riemann-Stieljes integration tools
as these are covered very incompletely these days.