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Positive measure and level sets of the Takagi function

  • Lai Jiang
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Abstract

Let T be the classical Takagi function, and L(y):={ x ∈ [0,1] : T(x) = y } be its level set at height y. For each positive integer m, let Sm be the set of y for which L(y) has exactly m points. We prove that S2n has positive Lebesgue measure for every positive integer n, confirming a conjecture of Allaart.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026positive,
  title = {{Positive measure and level sets of the Takagi function}},
  author = {Lai Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34377},
  eprint = {2609.34377},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34377},
}
RIS
TY  - UNPB
TI  - Positive measure and level sets of the Takagi function
AU  - Lai Jiang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34377
UR  - https://arxiv.org/abs/2609.34377
AB  - Let T be the classical Takagi function, and L(y):={ x ∈ [0,1] : T(x) = y } be its level set at height y. For each positive integer m, let S_m be the set of y for which L(y) has exactly m points. We prove that S_2n has positive Lebesgue measure for every positive integer n, confirming a conjecture of Allaart.
ER  -