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In mathematics, integrability is a property of certain dynamical systems.While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space.
Uniform integrability is an extension to the notion of a family of functions being dominated in which is central in dominated convergence. Several textbooks on real analysis and measure theory use the following definition: [1] [2] Definition A: Let (,,) be a positive measure space.
The cover of The Peter Principle (1970 Pan Books edition). The Peter principle is a concept in management developed by Laurence J. Peter which observes that people in a hierarchy tend to rise to "a level of respective incompetence": employees are promoted based on their success in previous jobs until they reach a level at which they are no longer competent, as skills in one job do not ...
In real analysis and measure theory, the Vitali convergence theorem, named after the Italian mathematician Giuseppe Vitali, is a generalization of the better-known dominated convergence theorem of Henri Lebesgue. It is a characterization of the convergence in L p in terms of convergence in measure and a condition related to uniform integrability.
Operational continuity refers to the ability of a system to continue working despite damages, losses, or critical events. In the Human Resources and Organizational domain, including IT, it implies the need to determine the level of resilience of the system, its ability to recover after an event, and build a system that resists to external and internal events or is able to recover after an ...
Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. [1] In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points.
Convergence of random variables, Convergence in mean; Monotone convergence theorem (does not require domination by an integrable function but assumes monotonicity of the sequence instead) Scheffé's lemma; Uniform integrability; Vitali convergence theorem (a generalization of Lebesgue's dominated convergence theorem)
Integrability may refer to: Bronshtein-integrability (informal) Frobenius integrability; Riemann-integrability; Lebesgue-integrability; see Lebesgue integral;