INTRODUCTION TO MEASURE AND INTEGRATION

A practical introduction for students or candidates looking to gain an understanding of measure and integration. This book covers key concepts, definitions, theorems and worked examples.

1.1 Introduction
1.2 Outer Lebesgue Measure of a Set
1.3 Lebesgue Measurable Set
1.4 Some More Definitions on Measurability
1.5 Measurable Functions
1.6 Properties of Measurable Functions
1.7 Concepts of Integrability
1.8 Lebesgue Integral of a Bounded Function
1.9 Lebesgue Integral for Bounded Functions Over a Subset of Real Numbers
1.10 General Lebesgue Integral
1.11 The Lebesgue Integral of Unbounded Functions