Mathematics · Real Analysis
Let f be a bounded function on [a, b]. Which of the following is the necessary and sufficient condition for f to be Riemann integrable on [a, b]?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f has only finite number of discontinuities
- 2For all ε > 0, there exists a partition P such that U(f, P) - L(f, P) < ε✓
- 3There exists a partition P such that U(f, P) = L(f, P)
- 4f is continuous on [a, b]
Correct answer
For all ε > 0, there exists a partition P such that U(f, P) - L(f, P) < ε
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