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 doing so …

Are Monotone functions Borel Measurable? Ask Question Asked 13 years ago Modified 5 years, 3 months ago

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 ?

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 why we need …

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 sequence …

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?

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 above, and a non …

Dec 15, 2019 · The monotone convergence theorem states for sequences of numbers that a monotonic and bounded sequence converges. Is there an analog for a sequence of uniformly-bounded, …

Sep 8, 2021 · I'm asked to give an example of a non-monotone function $ f : \mathbb R \to \mathbb R $ which has an inverse function. As far as I know, a function has an inverse if $ f ( x ) $ is one-to-one …