Real analysis or real number analysis is a mathematical analysis dealing with real numbers and real functions. Majors study series, series limit, differential, integral and function series, as well as the continuity and smoothness of real functions and other related properties.

Real analysis often begins with basic set theory, definition of function concept and so on.

The main contents of real analysis are Lebesgue measure and Lebesgue integral, as well as some related indefinite integrals and differentials.

You can refer to Peking University Zhou Minqiang's Theory of Real Variable Functions, which is divided into six chapters: set and point set, Lebesgue measure, measurable function, Lebesgue integral, differential, indefinite integral and Lp space.

Measure theory is an important and basic content of real analysis.

Functional analysis is a branch of mathematics juxtaposed with real analysis.