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 …

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 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?

Explore related questions real-analysis analysis functions monotone-functions See similar questions with these tags.

May 24, 2020 · I am watching a very nice set of videos on measure theory, which are great. But I am not clear on what the motivation is behind the monotone convergence theorem--meaning …

Jun 2, 2020 · I can understand that if $f$ is monotone, then $g$ is monotone by continuous inverse theorem. But is this really necessary for the inverse function theorem to be used?

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

Jan 26, 2013 · Show that a divergent monotone increasing sequence converges to $+\infty$ in this sense. I am having trouble understanding how to incorporate in my proof the fact that the …

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

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 …