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

• Autorzy: Rafał M. Łochowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26A45: Functions of bounded variation, generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 121-138

Daty

wydano

2013

Twórcy

autor

Rafał M. Łochowski

• Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Madalińskiego 6/8, 02-513 Warszawa, Poland
• African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg 7945, South Africa

Identyfikatory

DOI

10.4064/cm132-1-10