logic - Meaning of "Monotone" in Monotone Disjunction
2021年6月11日 · 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 ...
Difference between Increasing and Monotone increasing function
2016年4月17日 · 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.
graph theory - Is there a more common term than "monotone" …
The critical complexity of all (monotone) Boolean functions and monotone graph properties. Information and Control, 67:212-222, 1985. The only important result that comes to mind using the other definition is this paper but the proof appears to go through using either definition.
real analysis - Monotone Class Theorem for Functions
2015年2月10日 · Monotone Class Theorem: Suppose $\mathcal A_0$ is an algebra, $\mathcal A$ is the smallest $\sigma ...
A function is convex if and only if its gradient is monotone.
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Convergence of monotone nets - Mathematics Stack Exchange
2019年1月13日 · monotone-functions; nets. The Overflow Blog Stack Gives Back 2024! Linked. 5. Limit superior is a cluster ...
functional analysis - Showing that: $A$ maximal monotone ...
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real analysis - Monotone+continuous but not differentiable ...
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.
sequences and series - Monotonically increasing vs Non …
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-increasing (or strictly decreasing) sequence converges if it is bounded below.
real analysis - Is this function completely monotone?
2022年3月13日 · There are lots of tricks and special cases that help determine whether a function is completely monotone, but as far as my research has reached, I could not settle the case for this specific function. It might be interesting to discover new methods of proving -- or disproving -- that a certain function is completely monotone.