Abstract
In this note we show that, in the case of bounded sets in metric spaces with some additional structure, the boundedness of a family of Lebesgue p-summable functions follow from a certain uniform limit norm condition. As a byproduct, the well known Riesz-Kolmogorov compactness theorem can be formulated only with one condition.
| Original language | English |
|---|---|
| Pages (from-to) | 135-139 |
| Number of pages | 5 |
| Journal | Annales Academiae Scientiarum Fennicae Mathematica |
| Volume | 42 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
Keywords
- Compactness
- Metric measure spaces
- Riesz-Kolmogorov theorem
ASJC Scopus subject areas
- Mathematics(all)