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On the Dirichlet Continuity of Functions
http://hdl.handle.net/10083/2315
http://hdl.handle.net/10083/231524f94fba-8012-47c5-9079-06b61860425e
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KJ00004830601.pdf (685.5 kB)
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| 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 |
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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. |
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| 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 |
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| 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 | ||||||
