Real Analysis

Using a progressive but flexible format, this book contains a series of independent chapters that show how the principles and theory of real analysis can be applied in a variety of settings—in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization.

Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure,

Using a progressive but flexible format, this book contains a series of independent chapters that show how the principles and theory of real analysis can be applied in a variety of settings—in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization.