Contents
Preface xi
Preface to the Second Edition xvii
Recipe for a one semester course and interdependence of the chapters xix
Notations used in the text xxi
Prologue. The length function 1
Chapter 1. Riemann integration 5
§1.1. The Riemann integral: A review 5
§1.2, Characterization of Riemann integrable functions 18
§1.3. Historical notes: The integral from antiquity to Riemann 30
§1.4. Drawbacks of the Riemann integral 36
Chapter 2. Recipes for extending the Riemann integral 45
§2.1. A function theoretic view of the Riemann integral 45
§2.2. Lebesgue's recipe 47
§2.3. Riesz-Daniel recipe 49
Chapter 3. General extension theory 51
§3.1. First extension 51
§3.2. Semi-algebra and algebra of sets 54
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