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.
|Number of pages||5|
|Journal||Annales Academiae Scientiarum Fennicae Mathematica|
|Publication status||Published - 2017|
- Metric measure spaces
- Riesz-Kolmogorov theorem
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