Books in the Series In Real Analysis series

The contemporary approach of J. Kurzweil and R. Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations.

Provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. This book contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.

 This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock–Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers.It is widely acknowledged that the biggest difficulty in defining a Henstock–Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of "intervals" in the abstract setting. In this book the author shows a creative and innovative way of defining "intervals" in measure spaces, and prove many interesting and important results including the well-known Radon–Nikodým theorem.

The book is primarily devoted to the theory of the Kurzweil-Stieltjes integral and its important applications in functional analysis and the theory of various kinds of generalized differential equations, including the dynamical equations on time scales.