bounded variation

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In mathematical analysis, 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 single variable, being of bounded variation means that the distance along the direction of y-axis (i.e. the distance calculated neglecting the contribution of motion along x-axis) traveled by an ideal point moving along the graph of the given function (which, under given hypothesis, is also a continuous path) has a finite value. For a continuous function of several variables, the meaning of the definition is the same, except for the fact that the continuous path to be considered cannot be the whole graph of the given function (which is an hypersurface in this case), but can be every intersection of the graph itself with a plane parallel to a fixed x-axis and to the y-axis
bounded variation

    الواصلة

    bound·ed va·ri·a·tion

    التركية النطق

    baundıd verieyşın

    النطق

    /ˈboundəd ˌverēˈāsʜən/ /ˈbaʊndəd ˌvɛriːˈeɪʃən/
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