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 …

Jun 24, 2016 · Strongly monotone and cocoercive Ask Question Asked 9 years, 5 months ago Modified 9 years, 5 months ago

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 …

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?

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...

Oct 7, 2017 · I am asked to prove a sequence is not monotone, the sequence is increasing, but not every term is greater than the preceding so I know by definition the sequence is not …

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 …

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 …