This paper is an important treatise on the theory of real functions. It is motivated by a study of Rogers and Taylor characterizing those interval functions which are absolutely continuous with respect to the [italic]s-dimensional Hausdorff measure. This leads naturally to inves…
"This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit o…
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of…
This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly. After illuminating the significance of the subject through an overview of its history, the reader is introduced to the sophisticated toolkit of…
Introduction -- Preliminaries -- The real numbers and completeness -- An inverse function theorem and its application -- Limits, sequences, and series -- Uniform continuity -- The Riemann integral -- Differentiation -- Sequences and series of functions -- The complex numbers and…
Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so sh…
Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so sh…