ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Cartesian product
Complex cartesian product
Real cartesian product
Real number collection
Descriptive statistic
Definition D5043
Real function arithmetic mean
Formulation 3
Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that
(i) \begin{equation} a < b \end{equation}
(ii) $f : [a, b] \to \mathbb{R}$ is a D1760: Riemann integrable real function
A D993: Real number $a \in \mathbb{R}$ is an arithmetic mean for $f$ if and only if \begin{equation} \int^b_a a \, d t = \int^b_a f(t) \, d t \end{equation}
Children
D4925: Euclidean real arithmetic mean