The relatively new concepts of the Henstock–Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock–Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Contents:

• Bochner Integral
• Dunford and Pettis Integrals
• McShane and Henstock–Kurzweil Integrals
• More on the McShane Integral
• Comparison of the Bochner and McShane Integrals
• Comparison of the Pettis and McShane Integrals
• Primitive of the McShane and Henstock–Kurzweil Integrals
• Generalizations of Some Integrals

“I can recommend this book for those seeking an overview of the concepts and results achieved during the past 15 years.”

“This book is carefully written and should be accessible to anyone with a basic knowledge of classical integration theory and elementary functional analysis. The book contains an extensive bibliography and should be useful to those with interests in Banach space integration.”