The Basic Existence Theorem of Riemann-Stieltjes Integral

Kazuhisa Nakasho, Keiko Narita, and Yasunari Shidama. "The Basic Existence Theorem of Riemann-Stieltjes Integral." Formalized Mathematics 24.4 (2016): 253-259. <http://eudml.org/doc/288038>.

@article{KazuhisaNakasho2016,
abstract = {In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].},
author = {Kazuhisa Nakasho, Keiko Narita, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {Riemann-Stieltjes integral; bounded variation; continuous function},
language = {eng},
number = {4},
pages = {253-259},
title = {The Basic Existence Theorem of Riemann-Stieltjes Integral},
url = {http://eudml.org/doc/288038},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Kazuhisa Nakasho
AU - Keiko Narita
AU - Yasunari Shidama
TI - The Basic Existence Theorem of Riemann-Stieltjes Integral
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 4
SP - 253
EP - 259
AB - In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].
LA - eng
KW - Riemann-Stieltjes integral; bounded variation; continuous function
UR - http://eudml.org/doc/288038
ER -