Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let the distribution function $CDF(X,t)$ of a random variable $X$ be defined as $0$ for $ t <0, \text{Cantor function}(t)$ for $t \ge 0$ and $ t \le 1, 1$ for $ t > 1$ (for example, see for the used definition). What is the characteristic function of $X$? It would be an example of the characteristic function of a singular distribution.

share|cite|improve this question

1 Answer 1

up vote 2 down vote accepted

This should probably be a comment but I'm 9 points short.

The answer's on wikepedia. It's $e^{\tfrac{it}2} \prod_{i=1}^\infty cos\left(\frac t{3i}\right)$.

I'm pretty sure there's no closed form of the infinite product.

share|cite|improve this answer
Can you kindly give a reference for the proof? – Mark Apr 17 '13 at 19:11
There's also a reference on the wikipedia page. The proof is on page 4. – user32372 Apr 17 '13 at 19:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.