Results 41 to 50 of about 337,654 (135)
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper introduces the concepts of approximate limit, approximate continuity, and approximate derivatives for fuzzy‐number‐valued functions and examines their fundamental properties. Also, the relationships between approximate limit, approximate derivative of fuzzy‐number‐valued functions, and their representations of λ‐level sets are investigated ...
Chao Ma +3 more
wiley +1 more source
A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups [PDF]
, 2022 We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We prove that k-approximate differentiability almost everywhere is equivalent to admitting a Lusin approximation by $C^{k}_{\mathbb{G}}$ maps.
Speight, Gareth +2 more
core
Second‐order regularity for degenerate p$p$‐Laplace type equations with log‐concave weights
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We consider weighted p$p$‐Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log‐concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second‐order estimates. For unbounded domains, we prove local estimates at the boundary.
Carlo Alberto Antonini +2 more
wiley +1 more source
Monotone versus non‐monotone projective operators
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 256-264, January 2025.Abstract For a class of operators Γ$\Gamma$, let |Γ|$|\Gamma |$ denote the closure ordinal of Γ$\Gamma$‐inductive definitions. We give upper bounds on the values of |Σ2n+11,mon|$|\Sigma ^{1,mon}_{2n+1}|$ and |Π2n+21,mon|$|\Pi ^{1,mon}_{2n+2}|$ under the assumption that all projective sets of reals are determined, significantly improving the known ...
J. P. Aguilera, P. D. Welch
wiley +1 more source
Normal spaces and the Lusin-Menchoff property [PDF]
, 1997 summary:We study the relation between the Lusin-Menchoff property and the $F_\sigma$-"semiseparation" property of a fine topology in normal spaces. Three examples of normal topological spaces having the $F_\sigma$-"semiseparation" property without the ...
Pyrih, Pavel, M. Laczkovich
core +1 more source
Carnot rectifiability and Alberti representations
Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.Abstract A metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability ...
G. Antonelli, E. Le Donne, A. Merlo
wiley +1 more source
Bayesian social aggregation with almost‐objective uncertainty
Theoretical Economics, Volume 19, Issue 3, Page 1351-1398, July 2024.We consider collective decisions under uncertainty, when agents have generalized Hurwicz preferences, a broad class allowing many different ambiguity attitudes, including subjective expected utility preferences. We consider sequences of acts that are “almost‐objectively uncertain” in the sense that asymptotically, all agents almost agree about the ...
Marcus Pivato, Élise Flore Tchouante
wiley +1 more source
Generalized N-property and Sard theorem for Sobolev maps
, 2012 I report on some recent extensions of the Lusin N-property and the Sard theorem for Sobolev maps, which have been obtained in a joint work with M. Csornyei, E. D'Aniello, and B. Kirchheim.
ALBERTI, GIOVANNI
core +1 more source
A geometric approach to second-order differentiability of convex functions [PDF]
, 2023 We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and convex bodies by ...
Cappello, Anthony +2 more
core
On sets of extreme functions for Fatou's theorem
, 2023 Bounded holomorphic functions on the disk have radial limits in almost every direction, as follows from Fatou's theorem. Given a zero-measure set $E$ in the torus $\mathbb T$, we study the set of functions such that $\lim_{r \to 1^{-}} f(r \, w)$ fails ...
Carando, Daniel +2 more
core