What exactly does it mean for a function to be "well-behaved"?
The short answer is that there is no "exact" meaning. Ideally, additional axioms are introduced to ensure that a certain function (or any mathematical object, for that matter) is "well-behaved" which, in effect, makes analysis easier. So, the meaning of "well-behaved" should be derived from those specific additional axioms.
Well-Behaved Function - GM-RKB - gabormelli.com
A Well-Behaved Function is a function in a relationship with some other function that is more difficult to analyze. Example(s): a Continuous Function in relation to a Discontinuous Function. a Differentiable Function in relation to a Non-Differentiable Function. See: Well-Behaved, Function, Pathological Function.
mathematical physics - Examples where an ill-behaved function …
In mathematical derivations of physical identities, it is often more or less implicitly assumed that functions are well behaved. One example are the Maxwell identities in thermodynamics which assume that the order of partial derivatives of the thermodynamic potentials is irrelevant so …
Pathological (mathematics) - Wikipedia
In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition, it is sometimes called well-behaved or nice.
ECN113 week 6 and 8 Flashcards - Quizlet
How do we find the utility-maximizing solution for well behaved vs not well behaved functions? Well-behaved: Set MRS = MRT (solve pair of simultaneous equations) Examples: Cobb-Douglas, Quasilinear Not well-behaved: Use reasoning and diagrams (Case-by-case basis) Examples: Perfect substitutes, Perfect complements
Well-behaved - Scientific Lib
In probability, events contained in the probability space's corresponding sigma-algebra are well-behaved, as are measurable functions. Unusually, the term could also be applied in a comparative sense: In calculus: Analytic functions are better-behaved than general smooth functions.
“Well-Behaved” Preferences and the Law of Diminishing MRS
In practice, we’ll often focus on a subset of preferences that we call “well-behaved,” which have the following characteristics: We’ll pretty much always be using continuous utility functions at this level, but we will see some cases of non-smooth functions.
Well Behaved Function: Definition & Physical Phenomenon
Jan 26, 2024 · A well-behaved function is a mathematical function that has a consistent and predictable behavior. This means that for a given input, the function will always produce the same output, and the function will not exhibit any strange or unexpected behavior.
Well-behaved statistic - Wikipedia
First Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated. [3] Second Definition: The statistic is monotonic, well-defined, and locally sufficient. [4]
Everything in the start of this lesson is technically about mappings of which functions are only a part. This makes no difference to you for the moment, however, so don’t try to understand the difference until it is presented at the end.
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