Metric functionals and weak convergence
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908393605693440 |
|---|---|
| author | Gutiérrez, Armando W. Nevanlinna, Olavi |
| author_facet | Gutiérrez, Armando W. Nevanlinna, Olavi |
| contents | We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric functionals and weak convergence Gutiérrez, Armando W. Nevanlinna, Olavi Functional Analysis Metric Geometry We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one. |
| title | Metric functionals and weak convergence |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2506.04154 |