Mathematics · Real Analysis

Let f : [0, 1] → ℝ be a monotonic function. Which of the following statements is NOT necessarily true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1f is a Borel measurable function
2f is a Lebesgue measurable function
3The set of discontinuities of f cannot contain a non-empty open set
4f is continuous on [0, 1]✓

Correct answer

f is continuous on [0, 1]

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Let f : [0, 1] → ℝ be a monotonic function. Which of the following statements is NOT necessarily true?

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Let f : [0, 1] → ℝ be a monotonic function. Which of the following statements is NOT necessarily true?

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