Monotonically controlled integrals
| Autor: | Ball, Thomas, Preiss, David |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The monotonically controlled integral defined by Bendov\'a and Mal\'y, which is equivalent to the Denjoy-Perron integral, admits a natural parameter $\alpha>0$ thereby leading to the whole scale of integrals called $\alpha$-monotonically controlled integrals. While the power of these integrals is easily seen to increase with increasing $\alpha$, our main results show that their exact dependence on $\alpha$ is rather curious. For $\alpha<1$ they do not even contain the Lebesgue integral, for $1\le\alpha\le 2$ they coincide with the Denjoy-Perron integral, and for $\alpha>2$ they are mutually different and not even contained in the Denjoy-Khintchine integral. Comment: Final version will appear in the Volume commemorating Solomon Marcus |
| Databáze: | arXiv |
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