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Article | REF: AF109 V1

Bounded Variation Functions

Author: Jean-Charles PINOLI

Publication date: May 10, 2025 | Lire en français

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7. Numerical functions with bounded variations of several variables

This section considers functions of several real (or complex) variables with real (or complex) vector values.

7.1 Definitions

Definition (total variation). Let U be a non-empty open of ℝn . The total variation of a function belonging to L1(U,ℝ) is defined as follows:

TV(f,U)  :=  sup{
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Numerical functions with bounded variations of several variables
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