On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field
The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these con...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Baghdad
2019-05-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2140 |
| _version_ | 1811308089734856704 |
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| author | Hassan H. Ebrahim Ibrahim S. Ahmed |
| author_facet | Hassan H. Ebrahim Ibrahim S. Ahmed |
| author_sort | Hassan H. Ebrahim |
| collection | DOAJ |
| description |
The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on field as a generalization of the concept of measure on field. Furthermore, we establish new concept related to - field noted by weakly null-additive on field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function on field and many of its properties and characterizations are given.
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| first_indexed | 2024-04-13T09:15:52Z |
| format | Article |
| id | doaj.art-b9b3db4d090d433d80d3f381e2a84972 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-13T09:15:52Z |
| publishDate | 2019-05-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-b9b3db4d090d433d80d3f381e2a849722022-12-22T02:52:44ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072019-05-0132210.30526/32.2.2140On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–fieldHassan H. EbrahimIbrahim S. Ahmed The objective of this paper is, first, study a new collection of sets such as field and we discuss the properties of this collection. Second, introduce a new concepts related to the field such as measure on field, outer measure on field and we obtain some important results deals with these concepts. Third, introduce the concept of null-additive on field as a generalization of the concept of measure on field. Furthermore, we establish new concept related to - field noted by weakly null-additive on field as a generalizations of the concepts of measure on and null-additive. Finally, we introduce the restriction of a set function on field and many of its properties and characterizations are given. https://jih.uobaghdad.edu.iq/index.php/j/article/view/2140: σ–field, measure on σ–field, monotone measure, null-additive. |
| spellingShingle | Hassan H. Ebrahim Ibrahim S. Ahmed On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field Ibn Al-Haitham Journal for Pure and Applied Sciences : σ–field, measure on σ–field, monotone measure, null-additive. |
| title | On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field |
| title_full | On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field |
| title_fullStr | On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field |
| title_full_unstemmed | On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field |
| title_short | On a New Kind of Collection of Subsets Noted by δ–field and Some Concepts Defined on δ–field |
| title_sort | on a new kind of collection of subsets noted by i´a€ field and some concepts defined on i´a€ field |
| topic | : σ–field, measure on σ–field, monotone measure, null-additive. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2140 |
| work_keys_str_mv | AT hassanhebrahim onanewkindofcollectionofsubsetsnotedbyiafieldandsomeconceptsdefinedoniafield AT ibrahimsahmed onanewkindofcollectionofsubsetsnotedbyiafieldandsomeconceptsdefinedoniafield |