Concise Introduction to Measure Theory, A
Mathematics Calculus Measure and Integration Real Functions
Imprint: Springer
2018
1st ed. 2018.
EISBN 3030032418
Preface.
1. Preliminaries.
2. Measure Space and Integral.
3. Properties of the Integral.
4. Construction of a Measure. 5. The Counting Measure.
6. Product Measures.
7. Differentiation.
8. The Cantor Set and Function.
Solutions.
References.
Index.
This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration. The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book. This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.
1. Preliminaries.
2. Measure Space and Integral.
3. Properties of the Integral.
4. Construction of a Measure. 5. The Counting Measure.
6. Product Measures.
7. Differentiation.
8. The Cantor Set and Function.
Solutions.
References.
Index.
This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration. The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book. This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.
