Article Contents
Article Contents

# A decomposition theorem for $BV$ functions

• The Jordan decomposition states that a function $f: R\to R$ is of bounded variation if and only if it can be written as the difference of two monotone increasing functions.
In this paper we generalize this property to real valued $BV$ functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa.
A counterexample is given which prevents further extensions.
Mathematics Subject Classification: Primary: 26B30, 26B35; Secondary: 28A75.

 Citation:

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