<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>

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

Gifu National College of Technology, Japan

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

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">We prove that basic arithmetic operations preserve continuity of functions.</abstract>

On the Continuity of Some Functions

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">We introduce the notions of the geometric interior and the centre of mass for subsets of real linear spaces. We prove a number of theorems concerning these notions which are used in the theory of abstract simplicial complexes.</abstract>

The Geometric Interior in Real Linear Spaces

<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces.</abstract>

Miscellaneous Facts about Open Functions and Continuous Functions

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

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

On the Continuity of Some Functions

The Geometric Interior in Real Linear Spaces

Miscellaneous Facts about Open Functions and Continuous Functions

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Tous les volumes et éditions dans cette revue

Formalized Mathematics

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

On Lp Space Formed by Real-Valued Partial Functions

On the Continuity of Some Functions

The Geometric Interior in Real Linear Spaces

Miscellaneous Facts about Open Functions and Continuous Functions

Chercher

Tous les volumes et éditions dans cette revue

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