Let f be a monotone function on the open interval (a,b). Then f is continuous except possibly at a countable number of points in (a,b). Assume f is increasing. Furthermore, assume (a,b) is bou...

Apr 17, 2016 · As I have always understood it (and various online references seem to go with this tradition) is that when one says a function is increasing or strictly increasing, they mean it is doing so …

Aug 28, 2023 · I'm reading "An introduction to measure theory" from Terry Tao and I'm stuck understanding part of the proof of the following theorem:(whole argument can be found in his weblog …

Jun 17, 2014 · Proving that a sequence is monotone and bounded Ask Question Asked 11 years, 5 months ago Modified 11 years, 5 months ago

A function is convex if and only if its gradient is monotone. Ask Question Asked 9 years, 8 months ago Modified 1 year, 6 months ago

Are Monotone functions Borel Measurable? Ask Question Asked 13 years ago Modified 5 years, 2 months ago

Oct 7, 2017 · I am asked to prove a sequence is not monotone, the sequence is increasing, but not every term is greater than the preceding so I know by definition the sequence is not monotone. I was …

Note that the Monotone Convergence Theorem applies regardless of whether the above interpretations: a non-decreasing (or strictly increasing) sequence converges if it is bounded above, and a non …

In words, it is a monotone class containing the algebra $\mathcal A$. Since $\mathcal M$ is the smallest monotone class containing $\mathcal A$, it must be contained in any other monotone class …

Jan 11, 2011 · Is there a continuous and monotone function that's nowhere differentiable ?