2021/04/10 by Thierry De Pauw, De Pauw, Thierry
Economics, Econometrics and Finance · Mathematics · #26B15 #28A75 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #math.CA #math.FA #msc:26B15 #msc:28A75
paper · pdf · doi:10.48550/arxiv.2104.04730
arXiv admin note: substantial text overlap with arXiv:1904.12276
arxiv created 2021/04/10 · openalex publication_date 2021/04/10 · arxiv updated 2021/04/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Letting A ⊂ ℝn be Borel measurable and W0 : A → \mathbbG(n,m) Lipschitzian, we establish that \limsupr → 0+ (Hm [ A ∩ B(x,r) ∩ (x+ W0(x))])/(α(m)rm) ≥ (1)/(2n), for Ln-almost every x ∈ A. In particular, it follows that A is Ln-negligible if and only if Hm(A ∩ (x+W0(x))=0, for Ln-almost every x ∈ A.