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...

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

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?

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 …

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 …

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 …

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 …

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 …

Jun 18, 2025 · The question is a bit silly. In economics there is usually more than one good. Utility functions over one quantity (e.g. money/wealth) are really only used when looking at risky …