Skip to content
DraconiticResearch
Search Sources API
185,139 studies31 sourcesUpdated 1 min ago
PreprintarXiv licencearXiv

The semicontinuity of dimensions of measures

  • Daiki Takagi
Open at sourcePDFDOICite

Abstract

In this paper, we consider certain uniformity conditions on the radii of balls. Under these conditions, we study the semicontinuity of the Hausdorff dimension of measures with respect to measured Gromov--Hausdorff convergence and box convergence. We also examine the semicontinuity of other dimensions of measures, which are similar to the Hausdorff dimension of measures.

Related

  1. Sharp Projection Bounds for Intermediate Dimensions of Measures
    Shengyang Zang, Yingyu Zhao, Yunhao Zhao +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Exact Endpoint Asymptotics and Almost-Sure Limits for Uniform Empirical Measures in Two Dimensions
    Weitao Huang, Renzhen Wang, Yichen Wu +1
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  3. Packing intermediate dimensions of measures and applications
    Nicolas Angelini
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  4. Quasiconvexity and Lower Semicontinuity in the Riemannian Setting
    Aurora Corbisiero, Chiara Leone, Carlo Mantegazza
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  5. Semicontinuity for families of power series II
    Gert-Martin Greuel, Gerhard Pfister
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{takagi2026semicontinuity,
  title = {{The semicontinuity of dimensions of measures}},
  author = {Daiki Takagi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39014},
  eprint = {2609.39014},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39014},
}
RIS
TY  - UNPB
TI  - The semicontinuity of dimensions of measures
AU  - Daiki Takagi
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39014
UR  - https://arxiv.org/abs/2609.39014
AB  - In this paper, we consider certain uniformity conditions on the radii of balls. Under these conditions, we study the semicontinuity of the Hausdorff dimension of measures with respect to measured Gromov--Hausdorff convergence and box convergence. We also examine the semicontinuity of other dimensions of measures, which are similar to the Hausdorff dimension of measures.
ER  -