On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg Functions

Abstract

For a real càdlàg function f and a positive constant c we find another càdlàg function, which has the smallest total variation pos- sible among all functions uniformly approximating f with accuracy c/2. The solution is expressed with the truncated variation, upward truncated variation and downward truncated variation introduced in [L1] and [L2]. They are always finite even if the total variation of f is infinite, and they may be viewed as the generalisation of the Hahn-Jordan decomposition for real càdlàg functions. We also present partial results for more general functions.

arXiv admin note: substantial text overlap with arXiv:1106.3199

Cited by in corpus (3)

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