AN INTRODUCTION TO
ANALYSIS AND INTEGRATION THEORY

The text is divided into four sections:

Part I begins with a contraction of the real number system using Cauchy sequences and an extension of these ideas to metric and normed linear ideas. Special topics, such as Ston-Weierstrass Theorem and the Baire Category Theorem, are included.

Part II contains a rigorous and detailed exposition of the Lebesgue Integral and measurable functions, including such topics as the Riemann Integral and differentiation. A unique feature is the discussion of alternate approaches to integration theory and the demonstration of teir equivalence.

Part III introduces Banach and Hilbert Spaces, Fourier Series, and linear functionals. The exposition includes all the classical theorems (Riesz-Fischer, Hahn-Banach, etc.) and a discussion of the Stieltzes Integral; examples are given throughout.

Part IV extends earlier results to abstract spaces, concluding with chapters on the Daniell Integral, measure spaces, and the Radon-Nikodym Theorem.

Originally published in 1971.