<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Riemann Integral of Functions from ℝ into Real Banach Space

Gifu National College of Technology Japan

This work was supported by JSPS KAKENHI 22300285 and 23500029

Formalized Mathematics

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...

Riemann Integral of Functions from ℝ into Real Banach Space

Publicado en línea: 01 jun 2013

Páginas: 145 - 152

DOI: https://doi.org/10.2478/forma-2013-0016

This content is open access.