Numerical functions with bounded variations of one variable
Bounded Variation Functions
Article REF: AF109 V1
Numerical functions with bounded variations of one variable
Bounded Variation Functions

Author : Jean-Charles PINOLI

Publication date: May 10, 2025 | Lire en français

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6. Numerical functions with bounded variations of one variable

This section considers functions of one real (or complex) variable with real (or complex) values.

6.1 Definition

A function is said to have bounded variation when it satisfies a certain variational regularity condition, introduced in 1881 by the French mathematician C. Jordan.

Definition (total variation). The total variation of a real-valued (or complex) function f defined on a closed, bounded interval I:=[a,b] from ...

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