Exercise 11.7

Question

Find a necessary and sufficient condition that $f \in \mathscr{R}(\alpha)$ on $[a,b]$.

Amit Awasthi · Accepted Answer

\begin{claim}
      Suppose $f \in \mathscr{R}(\alpha)$ is bounded. Then $f \in
      \mathscr{R}(\alpha)$ on $[a,b]$ if and only if it is continuous
      $\alpha$-almost everywhere on $[a,b]$.
    \end{claim}
    \begin{proof}
      The proof is identical to Theorem $11.33$.
\end{proof}

Exercise 11.7

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Exercise 11.7

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