Integrability of Multivariable Continuous Functions

Noboru Endou; Yasunari Shidama

doi:10.2478/forma-2025-0015

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Integrability of Multivariable Continuous Functions

Formalized Mathematics

Volume 33 (2025): Issue 1 (September 2025)

By: Noboru Endou and Yasunari Shidama

Open Access

|Dec 2025

Abstract

In this article, we prove the integrability of continuous functions on n-dimensional real normed spaces, using the Mizar formalism. Generalizing selected theorems from the Mizar Mathematical Library, we prove the integrability of continuous real n-variable functions and then, using the correspondence between product-type and tuple-type spaces, we demonstrate the integrability of continuous functions on the desired multidimensional spaces.

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2025-0015 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 185 - 206

Submitted on: Nov 3, 2024

Accepted on: Dec 12, 2025

Published on: Dec 31, 2025

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

n-dimensional normed space,

product measure,

Lebesgue integration

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2025 Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 33 (2025): Issue 1 (September 2025)