# Remark on a theorem of Tonelli

In: Tatra Mountains Mathematical Publications, vol. 81, no. 1
Detaily:
Rok, strany: 2022, 89 - 92
Kľúčové slová:
surface area, bounded variation, Baire category
Typ článku: Real Functions
Typ dokumentu: scientific paper pdf
O článku:
It is well known that if the surface $f:[-1,1]×[-1,1]\to\mathbb{R}$ has a finite area, then the total variations of both sections $fx(y)=f(x,y)$ and $fy(x)=f(x,y)$ of $f$ are finite almost everywhere in $[-1,1]$. In the note it is proved that these variations can be infinite on residual subsets of $[-1,1]$.
Ako citovať:
ISO 690:
Wilczyński, W. 2022. Remark on a theorem of Tonelli. In Tatra Mountains Mathematical Publications, vol. 81, no.1, pp. 89-92. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0006

APA:
Wilczyński, W. (2022). Remark on a theorem of Tonelli. Tatra Mountains Mathematical Publications, 81(1), 89-92. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0006
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 22. 11. 2022
Verejná licencia: