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  1. 紀要
  2. お茶の水女子大學自然科學報告
  3. 36(1)

On the Dirichlet Continuity of Functions

http://hdl.handle.net/10083/2315
http://hdl.handle.net/10083/2315
24f94fba-8012-47c5-9079-06b61860425e
名前 / ファイル ライセンス アクション
KJ00004830601.pdf KJ00004830601.pdf (685.5 kB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2008-04-30
タイトル
タイトル On the Dirichlet Continuity of Functions
言語
言語 eng
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
著者 Iseki, Kanesiroo

× Iseki, Kanesiroo

WEKO 70292

Iseki, Kanesiroo

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著者(ヨミ)
識別子Scheme WEKO
識別子 70293
姓名 イセキ, カネシロオ
内容記述
内容記述タイプ Other
内容記述 This paper, which is a supplement to our recent work [5] on the powerwise integration, consists of three mutually independent sections, each being concerned, respectively, with elucidating a doubtful point contained explicitly or implicitly in the paper [5]. As defined in [5], a function is called Dirichlet continuous on a compact nonconnected set Q, if it is continuous on Q and if it fulfils the Dirichlet condition on every compact nonconnected set contained in Q. Now the definition of the Dirichlet condition consists of three items. We are interested in examining whether or not the second item is superfluous. The answer is in the negative, as will be shown in § 1. As defined in [5], a function is said to fulfil the condition (P) on a linear set E, if either the function is AC on E, or else if there exists a CT null set which contains E and on which the function is Dirichlet continuous. It is the object of § 2 to show that the Dirichlet continuity cannot be replaced here by the Dirichlet condition, in the sense that the theory of the powerwise integration would collapse if we did so. We thus find that the Dirichle\
t continuity is essentially stronger than the Dirichlet condition. We proposed in [5] the following problem : To decide whether a function which is Dirichlet continuous on a compact nonconnected set, is necessarily powerwise continuous on this set. This problem will be solved in the negative in § 3. As in our previous papers, a function, by itself, will always mean a mapping of the real line R into itself, unless another meaning is obvious from the context. We shall also continue denoting by N the set of the positive integers and by M that of the nonnegative integers.
書誌情報 お茶の水女子大學自然科學報告

巻 36, 号 1, p. 1-13, 発行日 1985-07
ISSN
収録物識別子タイプ ISSN
収録物識別子 00298190
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AN00033958
フォーマット
内容記述タイプ Other
内容記述 application/pdf
形態
685524 bytes
日本十進分類法
主題Scheme NDC
主題 400
出版者
出版者 お茶の水女子大学
資源タイプ
内容記述タイプ Other
内容記述 紀要論文
資源タイプ・ローカル
紀要論文
資源タイプ・NII
Departmental Bulletin Paper
資源タイプ・DCMI
text
資源タイプ・ローカル表示コード
03
所属
Department of Mathematics, Ochanomizu University
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