Only Transcendentals Known
Calculus
Level
4
Consider all functions \( f: \mathbb{R} \to \mathbb{R} \) satisfying that
- \(f(x) = 0\) for all transcendental numbers \(x\),
- the Lebesgue-integral \( \displaystyle \int_{-\infty}^{\infty} f(t) \, dt \) exists.
Let \( S = \left\{ \displaystyle \int_{-\infty}^{\infty} f(t) \, dt \right\} \). Which of the following describes \( S \)?
by
Deeparaj Bhat