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 …

A function is convex if and only if its gradient is monotone. Ask Question Asked 9 years, 7 months ago Modified 1 year, 5 months ago

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 …

Feb 22, 2018 · In every textbook or online paper I read, the proof of continuity of probability measure starts by assuming a monotone sequence of sets $(A_n)$. Or it assumes the $\\liminf …

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 …

Are Monotone functions Borel Measurable? Ask Question Asked 12 years, 11 months ago Modified 5 years, 1 month ago

Apr 10, 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 …

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 …

Mar 25, 2019 · Monotone convergence theorem of random variables and its example Ask Question Asked 6 years, 7 months ago Modified 6 years, 7 months ago

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