<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">This article is the continuation of [31]. We define the set of <italic>Lp</italic> integrable functions - the set of all partial functions whose absolute value raised to the <italic>p</italic>-th power is integrable. We show that <italic>Lp</italic> integrable functions form the <italic>Lp</italic> space. We also prove Minkowski's inequality, Hölder's inequality and that <italic>Lp</italic> space is Banach space ([15], [27]).</abstract>

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]).

On <italic>Lp</italic> Space Formed by Real-Valued Partial Functions

Graduate School of Science and Technology, Shinshu University, Nagano, Japan

Gifu National College of Technology, Japan

Formalized Mathematics

On  Space Formed by Real-Valued Partial Functions

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...

On L^p Space Formed by Real-Valued Partial Functions

Online veröffentlicht: 05. Jan. 2011

Seitenbereich: 159 - 169

DOI: https://doi.org/10.2478/v10037-010-0018-6

This content is open access.

On Lp Space Formed by Real-Valued Partial Functions

Online veröffentlicht: 05. Jan. 2011

Seitenbereich: 159 - 169

DOI: https://doi.org/10.2478/v10037-010-0018-6

This content is open access.

On L^p Space Formed by Real-Valued Partial Functions