On integrability in F-spaces
Studia Mathematica, Tome 110 (1994) no. 3, pp. 205-220
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable $l_p$-valued function (0 p 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable functions which tends to x uniformly and for which the sequence of derivatives tends to y uniformly. There is also constructed a differentiable function x with $x'(t_0) = x_0$ for given $t_0$ and $x_0$ and x'(t) = 0 for $t ≠ t_0$.
@article{10_4064_sm_110_3_205_220,
author = {Mikhail M. Popov},
title = {On integrability in {F-spaces}},
journal = {Studia Mathematica},
pages = {205--220},
publisher = {mathdoc},
volume = {110},
number = {3},
year = {1994},
doi = {10.4064/sm-110-3-205-220},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-110-3-205-220/}
}
Mikhail M. Popov. On integrability in F-spaces. Studia Mathematica, Tome 110 (1994) no. 3, pp. 205-220. doi: 10.4064/sm-110-3-205-220
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