Robert G. Bartle – författare

Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.

Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: Introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.

Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.

Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results—the convergence theorems.

A strong foundation in real analysis gives students a broadly-applicable skill set in deductive reasoning and analytical math, strengthening the creative thought processes required to extend ideas to new situations. Now in its fourth edition, Introduction to Real Analysis provides a rigorous and comprehensive introduction to the fundamentals of this versatile area of mathematics. Acknowledging the field''s increasing importance across disciplinary boundaries, this text relates real analysis concepts and methods to applications in a variety of fields.

Extensive use of examples and exercises underscores the necessity of hands-on learning and independent practice, while detailed appendices and early review chapters help students strengthen individual weaknesses to improve comprehension of new material. In-depth discussions surrounding sequences and series ensure a firm grasp of this fundamental topic, as these principles underlie much of the material that follows.