Construction of the real numbers
The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set (
Order properties of … See more

Various ideas from real analysis can be generalized from the real line to broader or more abstract contexts. These generalizations link … See more

• Athreya, Krishna B.; Lahiri, Soumendra N. (2006), Measure theory and probability theory, Springer, ISBN 0-387-32903-X
• Nielsen, Ole A. (1997), An introduction to integration and … See more

• How We Got From There to Here: A Story of Real Analysis by Robert Rogers and Eugene Boman
• A First Course in Analysis by Donald Yau
• Analysis WebNotes by John Lindsay Orr See more

Important results include the Bolzano–Weierstrass and Heine–Borel theorems, the intermediate value theorem and mean value theorem, Taylor's theorem, the fundamental theorem of calculus, the Arzelà-Ascoli theorem, the Stone-Weierstrass … See more

• List of real analysis topics
• Time-scale calculus – a unification of real analysis with calculus of finite differences
• Real multivariable function
• Real coordinate space See more

• Abbott, Stephen (2001). Understanding Analysis. Undergraduate Texts in Mathematics. New York: Springer-Verlag. ISBN See more