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-# Lecture 14
+# Math 4121 Lecture 14
+
+## Recap
+
+### Hankel developedn Riemann's integrabilty criterion.
+
+#### Definition 
+
+Given an interval $I\subset[a,b]$, $f:[a,b]\to\mathbb{R}$ the oscillation of $f$ at $I$ is
+
+$$
+\omega(f,I) = \sup_I f - \inf_I f
+$$
+
+#### Theorem 
+
+A bounded function $f$ is Riemann integrable if and only if
+
+