article · Mathematika · 2026

Graph‐null sets

Cited by 0Open access

Abstract

Abstract We say that a plane set is graph‐null , if there is a function such that . A plane set has the translational Kakeya property if, for every translated copy of and for every , there is a finite sequence of vertical and horizontal translations bringing to such that the area touched during the horizontal translations is less than . These properties are equivalent if is compact. We show that the graph of every absolutely continuous function is graph‐null. Also, the graph of a typical continuous function is graph‐null. Therefore, there are nowhere differentiable continuous functions whose graphs are graph‐null. Still, we show that there exists a continuous function whose graph is not graph‐null.

Cite this paper

APA 7

Laczkovich, M., & Máthé, A. (2026). Graph‐null sets. Mathematika, 72(4). https://doi.org/10.1112/mtk.70130

MLA 9

Laczkovich, Miklós, and A. Máthé. “Graph‐null sets.” Mathematika, vol. 72, no. 4, 2026, https://doi.org/10.1112/mtk.70130.

Chicago

Laczkovich, Miklós, and A. Máthé. 2026. “Graph‐null sets.” Mathematika 72 (4). https://doi.org/10.1112/mtk.70130.

Harvard

Laczkovich, M. and Máthé, A. (2026) ‘Graph‐null sets’, Mathematika, 72(4). Available at: https://doi.org/10.1112/mtk.70130.

BibTeX

@article{laczkovich2026graph,
  title = {{Graph‐null sets}},
  author = {Laczkovich, Miklós and Máthé, A.},
  journal = {Mathematika},
  volume = {72},
  number = {4},
  year = {2026},
  doi = {10.1112/mtk.70130}
}

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