On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions

Rafał M. Łochowski. "On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions." Colloquium Mathematicae 132.1 (2013): 121-138. <http://eudml.org/doc/283718>.

@article{RafałM2013,
abstract = {For a real càdlàg function f and a positive constant c we find another càdlàg function which has the smallest total variation among all functions uniformly approximating f with accuracy c/2. The solution is expressed in terms of truncated variation, upward truncated variation and downward truncated variation introduced in earlier work of the author. They are always finite even if the total variation of f is infinite, and they may be viewed as a generalisation of the Hahn-Jordan decomposition for real càdlàg functions. We also present partial results for more general functions.},
author = {Rafał M. Łochowski},
journal = {Colloquium Mathematicae},
keywords = {cádlág function; total variation; truncated variation; uniform approximation; regulated function},
language = {eng},
number = {1},
pages = {121-138},
title = {On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions},
url = {http://eudml.org/doc/283718},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Rafał M. Łochowski
TI - On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 121
EP - 138
AB - For a real càdlàg function f and a positive constant c we find another càdlàg function which has the smallest total variation among all functions uniformly approximating f with accuracy c/2. The solution is expressed in terms of truncated variation, upward truncated variation and downward truncated variation introduced in earlier work of the author. They are always finite even if the total variation of f is infinite, and they may be viewed as a generalisation of the Hahn-Jordan decomposition for real càdlàg functions. We also present partial results for more general functions.
LA - eng
KW - cádlág function; total variation; truncated variation; uniform approximation; regulated function
UR - http://eudml.org/doc/283718
ER -