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 …

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 …

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 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 …

A function is convex if and only if its gradient is monotone. Ask Question Asked 9 years, 8 months ago Modified 1 year, 5 months ago

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 7, 2021 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

Apr 3, 2015 · A monotone function never has saddle points, same is true for an invertible function. Can we conclude that monotonic function is also invertible and vice-versa?

Nov 22, 2022 · Adapting this proof math.stackexchange.com/questions/3996183/… to the strongly monotone $C^1$ case is very straightforward, you just need to use strong monotonicity …

Apr 9, 2015 · In my Economics class, we are talking about monotonic transformations of ordered sets. But I don't understand how I can tell if a given function will preserve the order. My …