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What (who) is bounded variation - definition
Bounded variation
![The function ''f''(''x'') = sin(1/''x'') is ''not'' of bounded variation on the interval <math> [0,2 / \pi] </math>.](https://commons.wikimedia.org/wiki/Special:FilePath/Sin x^-1.svg?width=200 "The function ''f''(''x'') = sin(1/''x'') is ''not'' of bounded variation on the interval <math> [0,2 / \pi] </math>.")
![The function ''f''(''x'') = ''x''<sup>2</sup> sin(1/''x'') ''is'' of bounded variation on the interval <math> [0,2 / \pi] </math>.](https://commons.wikimedia.org/wiki/Special:FilePath/X^2sin(x^-1).svg?width=200 "The function ''f''(''x'') = ''x''<sup>2</sup> sin(1/''x'') ''is'' of bounded variation on the interval <math> [0,2 / \pi] </math>.")
![The function ''f''(''x'') = ''x'' sin(1/''x'') is ''not'' of bounded variation on the interval <math> [0,2 / \pi] </math>.](https://commons.wikimedia.org/wiki/Special:FilePath/Xsin(x^-1).svg?width=200 "The function ''f''(''x'') = ''x'' sin(1/''x'') is ''not'' of bounded variation on the interval <math> [0,2 / \pi] </math>.")
REAL FUNCTION WITH FINITE TOTAL VARIATION
Function variation; Function of bounded variation; BV function; Bv function; Bv space; SBV function; SBV functions
In mathematical analysis, a function of bounded variation, also known as function, is 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 single variable, being of bounded variation means that the distance along the direction of the -axis, neglecting the contribution of motion along -axis, traveled by a point moving along the graph has a finite value.
variation
WIKIMEDIA DISAMBIGUATION PAGE
Variations; Varied; Varying; Variation (disambiguation); Viccitude; Variations (album); Variation (combinatorics); Variations (Combinatorics); Variation (Combinatorics)
¦ noun
1. a change or slight difference in condition, amount, or level.
(also magnetic variation) the angular difference between true north and magnetic north at a particular place.
2. a different or distinct form or version.
Music a new but still recognizable version of a theme.
Ballet a solo dance as part of a performance.
Derivatives
variational adjective
varied
WIKIMEDIA DISAMBIGUATION PAGE
Variations; Varied; Varying; Variation (disambiguation); Viccitude; Variations (album); Variation (combinatorics); Variations (Combinatorics); Variation (Combinatorics)
¦ adjective incorporating a number of different types or elements; showing variation or variety.
Derivatives
variedly adverb
