2023/03/02 by Harrison Gaebler, Gaebler, Harrison, Bünyamin Sarı +1
Economics, Econometrics and Finance · Mathematics · #46B20 #46G12 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Housing Market and Economics #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2303.01434
openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Banach space is said to have the Lebesgue property if every Riemann-integrable function f:[0,1]→ X is Lebesgue almost everywhere continuous. We give a characterization of the Lebesgue property in terms of a new sequential asymptotic structure that is strictly between the notions of spreading and asymptotic models. We also reproduce an apparently lost theorem of Pelczynski and da Rocha Filho that a subspace X⊂ L1[0,1] has the Lebesgue property if every spreading model of X is equivalent to the unit vector basis of ℓ1.