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Bounded variation

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  • Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… …   Wikipedia

  • Variation — means a change within population* Biodiversity * Genetic diversity, differences within a speciesPhysics: * Magnetic variation, difference between magnetic north and true north, measured as an angle * Variation (astronomy), any perturbation of the …   Wikipedia

  • Bounded deformation — In mathematics, a function of bounded deformation is a function whose distributional derivatives are not quite well behaved enough to qualify as functions of bounded variation, although the symmetric part of the derivative matrix does meet that… …   Wikipedia

  • bounded — boundedly, adv. boundedness, n. /bown did/, adj. 1. having bounds or limits. 2. Math. a. (of a function) having a range with an upper bound and a lower bound. b. (of a sequence) having the absolute value of each term less than or equal to some… …   Universalium

  • Total variation — As the green ball travels on the graph of the given function, the length of the path travelled by that ball s projection on the y axis, shown as a red ball, is the total variation of the function. In mathematics, the total variation identifies… …   Wikipedia

  • Quadratic variation — In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process. Definition Suppose that X t is a real valued stochastic… …   Wikipedia

  • Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… …   Wikipedia

  • Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

  • Caccioppoli set — In mathematics, a Caccioppoli set is a set whose boundary is measurable and has a finite measure . A synonym is set of finite perimeter. Basically, a set is a Caccioppoli set if its characteristic function is a function of bounded variation.… …   Wikipedia

  • Helly's selection theorem — In mathematics, Helly s selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence. In other words, it is a compactness theorem for the space… …   Wikipedia

  • Absolute continuity — In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using… …   Wikipedia