On Lp Space Formed by Real-Valued Partial Functions

Yasushige Watase; Noboru Endou; Yasunari Shidama

doi:10.2478/v10037-010-0018-6

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On Lp Space Formed by Real-Valued Partial Functions

Formalized Mathematics

Volume 18 (2010): Issue 3 (September 2010)

By: Yasushige Watase, Noboru Endou and Yasunari Shidama

Open Access

|Jan 2011

Abstract

This article is the continuation of [31]. We define the set of L^p integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that L^p integrable functions form the L^p space. We also prove Minkowski's inequality, Hölder's inequality and that L^p space is Banach space ([15], [27]).

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Articles in this issue

DOI: https://doi.org/10.2478/v10037-010-0018-6 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 159 - 169

Published on: Jan 5, 2011

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2011 Yasushige Watase, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 18 (2010): Issue 3 (September 2010)