ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Binary endorelation
Preordering relation
Partial ordering relation
Partially ordered set
Closed interval
Implicit interval partition
Implicit basic real interval partition
Closed real interval tagged partition
Stieltjes sum
Riemann sum
Riemann integrable real function
Real Riemann integral
Standard natural real logarithm function
Standard real logarithm function
Definition D5706
Real entropy function
Formulation 0
The real entropy function in base $a \in (0, \infty)$ is the D4364: Real function \begin{equation} (0, \infty) \to \mathbb{R}, \quad x \mapsto x \log_a x \end{equation}