1
$\begingroup$

If $f\colon [0,1]\to\Bbb R$ is a continuous function and differentiable on (0,1), then which of the following is correct?

  1. $f'$ is Borel and Lebesgue measurable.
  2. $f'$ is Borel measurable and is not Lebesgue measurable.
  3. $f'$ is not Borel measurable and is not Lebesgue measurable.
  4. $f'$ is not Borel measurable and is Lebesgue measurable.
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

This might help.

$$f'(x) = \lim_{n\to\infty} n(f(x + 1/n) - f(x)).$$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .