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

Keiko Narita; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2013)

- Volume: 21, Issue: 3, page 185-191
- ISSN: 1426-2630

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topKeiko Narita, Noboru Endou, and Yasunari Shidama. "The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space." Formalized Mathematics 21.3 (2013): 185-191. <http://eudml.org/doc/266690>.

@article{KeikoNarita2013,

abstract = {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.},

author = {Keiko Narita, Noboru Endou, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {formalization of Riemann integral},

language = {eng},

number = {3},

pages = {185-191},

title = {The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space},

url = {http://eudml.org/doc/266690},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Keiko Narita

AU - Noboru Endou

AU - Yasunari Shidama

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

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 3

SP - 185

EP - 191

AB - 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.

LA - eng

KW - formalization of Riemann integral

UR - http://eudml.org/doc/266690

ER -

## References

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