Real analysis

the long version

"Aimed at advanced undergraduates and beginning graduate students, Real Analysis offers a rigorous yet accessible course in the subject. Carothers, presupposing only a modest background in real analysis or advanced calculus, writes with an informal style and incorporates historical commentary as well as notes and references." "The book looks at metric and linear spaces, offering an introduction to general topology while emphasizing normed linear spaces. It addresses function spaces and provides familiar applications, such as the Weierstrass and Stone-Weierstrass approximation theorems, functions of bounded variation, Riemann-Stieltjes integration, and a brief introduction to Fourier analysis. Finally, it examines Lebesgue measure and integration on the line. Illustrations and abundant exercises round out the text." "Real Analysis will appeal to students in pure and applied mathematics as well as researchers in statistics, education, engineering, and economics."--Jacket.