Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $ f: \mathbb R \to \mathbb R $ a non-negative bounded measurable function. Prove that there exists a sequence of simple non-negative functions $ (f_n)_{n \in \mathbb N} $ such that $ f_n \to f$ uniform.

Searching on Wikipedia I found the following http://en.wikipedia.org/wiki/Simple_function

but I can't understand why the converge is uniform.

Any help?

share|improve this question
    
The key point behind the uniform part of this statement lies in the boundedness of $f$. –  Thomas E. Jun 28 '12 at 18:53

1 Answer 1

Hint: if $A \le f \le B$, split up $[A,B]$ into $n$ equal intervals and choose a value for $f_n$ in each one.

share|improve this answer

Your Answer

 
discard

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.