Editing List of real analysis topics (section)

==Applied mathematical tools==

===[[Infinite expression (mathematics)|Infinite expressions]]===

*[[Continued fraction]]
*[[Series (mathematics)|Series]]
*[[Infinite product]]s

===[[Inequality (mathematics)|Inequalities]]===
''See [[list of inequalities]]''

*[[Triangle inequality]]
*[[Bernoulli's inequality]]
*[[Cauchy–Schwarz inequality]]
*[[Hölder's inequality]]
*[[Minkowski inequality]]
*[[Jensen's inequality]]
*[[Chebyshev's inequality]]
*[[Inequality of arithmetic and geometric means]]

===[[Mean]]s===
*[[Generalized mean]]
*[[Pythagorean means]]
**[[Arithmetic mean]]
**[[Geometric mean]]
**[[Harmonic mean]]
*[[Geometric–harmonic mean]]
*[[Arithmetic–geometric mean]]
*[[Weighted mean]]
*[[Quasi-arithmetic mean]]

===[[Orthogonal polynomials]]===

*[[Classical orthogonal polynomials]]
**[[Hermite polynomials]]
**[[Laguerre polynomials]]
**[[Jacobi polynomials]]
**[[Gegenbauer polynomials]]
**[[Legendre polynomials]]

===[[Space (mathematics)|Spaces]]===

*[[Euclidean space]]
*[[Metric space]]
**[[Banach fixed point theorem]] – guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, provides method to find them
**[[Complete metric space]]
*[[Topological space]]
**[[Function space]]
***[[Sequence space]]
*[[Compact space]]

===[[Measure (mathematics)|Measures]]===

*[[Lebesgue measure]]
*[[Outer measure]]
**[[Hausdorff measure]]
*[[Dominated convergence theorem]] – provides sufficient conditions under which two limit processes commute, namely Lebesgue integration and almost everywhere convergence of a sequence of functions.

===[[Field of sets]]===

*[[Sigma-algebra]]