Riemann Integral of Functions from ℝ into Real Banach Space

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

Abstrakty

EN

In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the convergence of sequences. We applied definitions introduced in the previous article [21] to the proof of integrability.

Słowa kluczowe

EN

formalization of Riemann integral

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2013
• Tom: 21
• Numer: 2
• Strony: 145-152

Daty

wydano

2013-06-01

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-2013-0016