This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).
@article{bwmeta1.element.doi-10_2478_v10037-010-0018-6,
author = {Yasushige Watase and Noboru Endou and Yasunari Shidama},
title = {
On
L
p
Space Formed by Real-Valued Partial Functions
},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {159-169},
zbl = {1283.46024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0018-6}
}
Yasushige Watase; Noboru Endou; Yasunari Shidama.
On
L
p
Space Formed by Real-Valued Partial Functions
. Formalized Mathematics, Tome 18 (2010) pp. 159-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0018-6/
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