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Difference between Increasing and Monotone increasing function 17 Apr 2016 · This largely echoes what was said by Thomas above, but, taking monotone as a term referring to the behavior of a function over the whole domain, one does not need to say "I'm used to." That said, one should always be clear on what definitions are being used as consistency is not a human's strong point.
logic - Meaning of "Monotone" in Monotone Disjunction 11 Jun 2021 · The set of slides you link to speaks of "monotone disjunctions" in a particular AI context, and the terse woirding "no negations" makes sense only in this implicit context. It is common in this area to consider disjunctive clauses of the form $$ x \lor y \lor \neg z \lor w \lor \cdots \lor \neg u $$ -- that is, a disjunction of input variables and/or negations of input variables.
Submodular monotone functions - Mathematics Stack Exchange A monotone submodular function is a submodular functions such that for every $ S,T \subseteq E $ with $ S ...
Convergence of monotone nets - Mathematics Stack Exchange 13 Jan 2019 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Is every monotone map the gradient of a convex function? 6 Jul 2016 · Secondly, convex functions are not necessarily differentiable; instead, they have a subdifferential, and the subdifferential map is monotone. So the broader question: when is a monotone map the subdifferential of a convex function? That's a good question and it was answered by the pioneer of convex analysis, Rockafellar.
Monotone convergence theorem for a sequence of measures? I seem to be able to verify it for simple functions. But the general case (using the plain monotone convergence theorem) involves switching limits of sequences and I'm not familiar with any conditions that allow this (specifically none that obviously apply here).
real analysis - Monotone Convergence for Decreasing Functions ... 9 Oct 2015 · As you say in the comments, the problem is posed at the end of the first chapter of Rudin's Real and Complex Analysis, so it is not clear whether Rudin intends the student to use the Monotone Convergence Theorem, Fatou's Lemma or the Dominated Convergence Theorem. You are right that the proof is a trivial application of DCT.
graph theory - Is there a more common term than "monotone" that ... In the context of property testing, we usually don't care about the distinction, since the negation of a monotone decreasing property is monotone increasing. But the distinction is there to be made. The definition you found on Wikipedia seems to also allow you to take subgraphs with fewer vertices, whereas usually you just consider subsets (and supersets) of the edge set and keep …
real analysis - Every sequence has a monotone subsequence Hence, any sequence has some subsequence that is monotone, whether increasing or decreasing. Share. Cite. ...
real analysis - Monotone+continuous but not differentiable ... 11 Jan 2011 · Even without the assumption of continuity, a monotone function on $\mathbb{R}$ is differentiable except on a set of measure $0$ (and it can have only countably many discontinuities). This is mentioned on Wikipedia , and proofs can be found in books on measure theory such as Royden or Wheeden and Zygmund.