ScholarLens Back to search
2019•Institutional Repositories DataBase (IRDB)Open access

Axiomatic Method of Measure and Integration (III). Definition and Existence Theorem of the Lebesgue Measure (Yoshifumi Ito “Theory of Lebesgue Integral”, Chapter 5)

Yoshifumi Ito

Open full text 0 citations

Abstract

In this paper, we define the Lebesgue measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the uniqueness and existence theorem of the Lebesgue measure. This is a new result.

About this research paper

What this paper is about

In this paper, we define the Lebesgue measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the uniqueness and existence theorem of the Lebesgue measure. This is a new result.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we define the Lebesgue measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the uniqueness and existence theorem of the Lebesgue measure. This is a new result.

Key concepts: Mathematics, Lebesgue–Stieltjes integration, Measure (data warehouse), Axiom, Lebesgue integration, Lebesgue measure, Lebesgue's number lemma, Riemann integral

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Axiomatic Method of Measure and Integration (III). Definition and Existence Theorem of the Lebesgue Measure (Yoshifumi Ito “Theory of Lebesgue Integral”, Chapter 5) — Research Paper | ScholarLens