Real Analysis

About this book

This text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory general topology and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic form and presented initially in a general setting. The Lebesgue-Stieltjes integral is introduced in terms of the ideas of Daniell measure-theoretic considerations playing only a secondary part. The final chapter on function spaces and harmonic analysis is deliberately accelerated. Helpful exercises appear throughout the text. 1959 edition.