Let $[a, b] \subset \mathbb{R}$ be a
D544: Closed real interval such that
| (i) |
\begin{equation}
a
< b
\end{equation}
|
| (ii) |
$f : [a, b] \to \mathbb{R}$ is a D4364: Real function on $[a, b]$
|
Then $f$ is a
Riemann integrable real function on $[a, b]$ if and only if
\begin{equation}
\exists \, R \in \mathbb{R} :
\forall \, \varepsilon > 0 :
\exists \, \delta > 0
\left( P \text{ is a tagged partition for } [a, b] \text{ with } \text{Mesh}(P) < \delta \quad \implies \quad \left| \mathcal{R}_P(f) - R \right| < \varepsilon \right)
\end{equation}
