Real Analysis for Graduate Students, version 2.1

Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination.

• Clarity: Every effort was made to present the material in as clear a fashion as possible.
• Lots of exercises: Over 400 exercises, ranging from routine to challenging, are presented. Many are taken from preliminary examinations given at major universities.
• Affordability: This book is priced at well under $15.

Topics covered include the definition and construction of measures, the Lebesgue integral and its properties, limit theorems, product measures, signed measures, the Radon-Nikoydym theorem, differentiation, L^p spaces, Fourier transforms, the Riesz representation theorem, and Banach and Hilbert spaces.