The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

• Autorzy: Keiko Narita , Noboru Endou , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

Słowa kluczowe

EN

formalization of Riemann integral

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2013
• Tom: 21
• Numer: 3
• Strony: 185-191

Daty

wydano

2013-10-01

Twórcy

autor

Keiko Narita

• Hirosaki-city Aomori, Japan

autor

Noboru Endou

• Gifu National College of Technology Japan

autor

Yasunari Shidama

• Shinshu University Nagano, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2013-0020