Geodesic
On a generalisation of the Banach Indicatrix Theorem
Rafał M. Łochowski 1
1 Department of Mathematics and Mathematical Economics Warsaw School of Economics Madalińskiego 6/8 02-513 Warszawa, Poland and African Institute for Mathematical Sciences 6-8 Melrose Road Muizenberg 7945, South Africa
Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 301-313 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that for any regulated function $f:[a,b]\rightarrow \mathbb {R}$ and $c\geq 0,$ the infimum of the total variations of functions approximating $f$ with accuracy $c/2$ is equal to $\int _{\mathbb {R}} n_{c}^{y} \,dy,$ where $n_{c}^{y}$ is the number of times $f$ crosses the interval $[y,y+c].$
DOI : 10.4064/cm6583-3-2017
Keywords: prove regulated function rightarrow mathbb geq infimum total variations functions approximating accuracy equal int mathbb where number times crosses interval

Rafał M. Łochowski  1

1 Department of Mathematics and Mathematical Economics Warsaw School of Economics Madalińskiego 6/8 02-513 Warszawa, Poland and African Institute for Mathematical Sciences 6-8 Melrose Road Muizenberg 7945, South Africa 
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Rafał M. Łochowski. On a generalisation of the Banach Indicatrix Theorem. Colloquium Mathematicum, Tome 148 (2017) no. 2, pp. 301-313. doi: 10.4064/cm6583-3-2017

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