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Introduction
Preface
1. Point-Set Topology
2. Functions of Bounded Variation and Rectifiable Curves
2.1. Functions of Bounded Variation
2.2. Total Variation
2.3. Continuous Functions of Bounded Variation
3. The Riemann-Stieltjes Integral
3.1. The Definition of the Riemann-Stieltjes Integral
3.2. Linear Properties
3.3. Integration by Parts
3.4. Change of Variables in Riemann-Stieltjes Integrals
3.5. Reduction to Riemann Integrals
3.6. Step Functions as Integrators
3.7. Reduction of Riemann-Stieltjes Integrals to Finite Sums
3.8. Euler’s Summation Formula
3.9. Darboux Integration – Defining Integrals with Upper and Lower Integrals
3.10. Additive and Linearity Properties of Upper and Lower Integrals
3.11. Riemann’s Condition
3.12. Comparison Theorems
3.13. Integrators of Bounded Variation
3.14. Sufficient Conditions for Existence of Riemann-Stieltjes Integrals
3.15. Necessary Conditions for Existence of Riemann-Stieltjes Integrals
3.16. Mean Value Theorems for Riemann-Stieltjes Integrals
Appendix
References
Index
.md
.pdf
Preface
Preface
#
This book mainly follows the structure of
[
Apostol, 1974
]
.
