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...

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 …

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 …

A function is convex if and only if its gradient is monotone. Ask Question Asked 9 years, 9 months ago Modified 1 year, 7 months ago

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

Feb 14, 2019 · ‎Let ‎ $‎f: [1, +‎\infty‎)‎‎‎\rightarrow‎‎\mathbb {R}$ ‎be a‎ ‎concave ‎function. Suppose‎ $‎F: [1, +‎\infty‎)‎‎\rightarrow‎‎\mathbb {R}‎$ is a primitive function of ‎ $‎f‎$ ‎. My ‎questions ‎are‎:‎ ‎‎ ‎ (a) ‎‎What …

Could you guide me how to prove that any monotone function from R → R R → R is Borel measurable? Since monotone functions are continuous away from countably many points, …

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 …

Oct 18, 2018 · Also in the german book "Nichtlineare Funktionalanalysis" by Ruzicka and in the following lecture notes, Theorem 9.13. Note that for a monotone operator demicontinuity and …