Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Noboru Endou"'
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics. 29:201-220
Summary In this article, we deal with Riemann’s improper integral [1], using the Mizar system [2], [3]. Improper integrals with finite values are discussed in [5] by Yamazaki et al., but in general, improper integrals do not assume that they are fi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eb3b76f842021870dbe265eb4b2be511
https://doi.org/10.2478/forma-2021-0019
https://doi.org/10.2478/forma-2021-0019
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics. 29:185-199
Summary The goal of this article is to clarify the relationship between Riemann and Lebesgue integrals. In previous article [5], we constructed a one-dimensional Lebesgue measure. The one-dimensional Lebesgue measure provides a measure of any interva
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::77f4895a1185ebaf6916693692fcb8e1
https://doi.org/10.2478/forma-2021-0018
https://doi.org/10.2478/forma-2021-0018
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics, Vol 28, Iss 1, Pp 93-104 (2020)
Summary In the Mizar system ([1], [2]), Józef Białas has already given the one-dimensional Lebesgue measure [4]. However, the measure introduced by Białas limited the outer measure to a field with finite additivity. So, although it satisfies the n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bcc0339d0a99d5ddba6b4582a01b8889
https://doaj.org/article/779e4c82818148978f9f1351715ae1dc
https://doaj.org/article/779e4c82818148978f9f1351715ae1dc
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics, Vol 27, Iss 1, Pp 67-74 (2019)
Summary Fubini theorem is an essential tool for the analysis of high-dimensional space [8], [2], [3], a theorem about the multiple integral and iterated integral. The author has been working on formalizing Fubini’s theorem over the past few years [
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43047a098848ef3622567fc65afe5374
https://doaj.org/article/63f3a0b903454e188f63c6e14c5c4bde
https://doaj.org/article/63f3a0b903454e188f63c6e14c5c4bde
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics, Vol 26, Iss 1, Pp 49-67 (2018)
Summary The goal of this article is to show Fubini’s theorem for non-negative or non-positive measurable functions [10], [2], [3], using the Mizar system [1], [9]. We formalized Fubini’s theorem in our previous article [5], but in that case we sh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d4553dd39da73545dc9faf400cf3413
https://doaj.org/article/605c379e5e284eabab79901d256b6e1c
https://doaj.org/article/605c379e5e284eabab79901d256b6e1c
Autor:
Noboru Endou1
Publikováno v:
Formalized Mathematics. Oct2017, Vol. 25 Issue 3, p227-240. 14p.
Autor:
Noboru Endou
Publikováno v:
Formalized Mathematics, Vol 24, Iss 1, Pp 69-79 (2016)
Summary In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b412ddc4cf4e5f2a9790160373d2efe1
https://doi.org/10.1515/forma-2016-0006
https://doi.org/10.1515/forma-2016-0006
Autor:
Kazuhisa Nakasho1, Noboru Endou2
Publikováno v:
Formalized Mathematics. Mar2015, Vol. 23 Issue 1, p59-65. 7p.
Publikováno v:
Formalized Mathematics. Mar2015, Vol. 23 Issue 1, p51-57. 7p.