Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2509.17426 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $ϕ(v; \cdot)$ be the density of the absolutely continuous part of a Radon measure $Φ(v; \cdot)$ associated to a function $v\colon X\rightarrow \mathbb{R}$ defined on the topological measure space $(X,λ)$. For concave $ζ\colon [0, \infty)\rightarrow[0,\infty)$ with $\lim_{t\to 0} ζ(t)=0$ and $\lim_{t\to\infty}ζ(t)/t= 0$, it is shown that the functional $v \mapsto \int_{X} ζ(ϕ(v;x))dλ(x)$ depends upper semicontinuously on $v$. Examples include functional affine surface areas for convex functions.