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# Real analysis

Show that $$f: [a,b] \to \mathbb R$$ is Riemann integrable on $$[a,b]$$ if and only if there exists $$L \in \mathbb R$$ such that for every $$\epsilon > 0$$ there exists $$\delta_{\epsilon} > 0$$ such that if $$\mathcal P$$ is any tagged partition with norm $$||\dot{\mathcal P} || \leq \delta_\epsilon$$, then $$| S ( f; \dot{\mathcal P}) - L | \leq \epsilon$$.

Note by Syed Subhan Siraj
1 year, 5 months ago