Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifyingexamination in real analysis. This book provides the necessary tools topass such an examination. Clarity: Every effort was made to present thematerial in as clear a fashion as possible. Lots of exercises: Over 400 exercises, rangingfrom routine to challenging, are presented. Many aretaken from preliminary examinations given at major universities. Affordability: This book is priced at wellunder $15. Topics covered include the definition and construction of measures, theLebesgue integral and its properties,limit theorems, product measures, signed measures,the Radon-Nikoydym theorem, differentiation,Lp spaces, Fourier transforms, theRiesz representation theorem, and Banach and Hilbert spaces.
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