Measures on coallocation and normal lattices
Let ℒ1 and ℒ2 be lattices of subsets of a nonempty set X. Suppose ℒ2 coallocates ℒ1 and ℒ1 is a subset of ℒ2. We show that any ℒ1-regular finitely additive measure on the algebra generated by ℒ1 can be uniquely extended to an ℒ2-regular measure on the algebra generated by ℒ2. The case when ℒ1 is not...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000929 |
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| _version_ | 1832554820998791168 |
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| author | Jack-Kang Chan |
| author_facet | Jack-Kang Chan |
| author_sort | Jack-Kang Chan |
| collection | DOAJ |
| description | Let ℒ1 and ℒ2 be lattices of subsets of a nonempty set X. Suppose ℒ2 coallocates ℒ1 and ℒ1 is a subset of ℒ2. We show that any ℒ1-regular finitely additive measure on the algebra generated by ℒ1 can be uniquely extended to an ℒ2-regular measure on the algebra generated by ℒ2. The case when ℒ1 is not necessary contained in ℒ2, as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given. |
| format | Article |
| id | doaj-art-10f634c629aa43fb9bb0a0d61c9c429c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-10f634c629aa43fb9bb0a0d61c9c429c2025-02-03T05:50:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115470171810.1155/S0161171292000929Measures on coallocation and normal latticesJack-Kang Chan0Norden Systems, 75 Maxess Road, Melville, New York 11747, USALet ℒ1 and ℒ2 be lattices of subsets of a nonempty set X. Suppose ℒ2 coallocates ℒ1 and ℒ1 is a subset of ℒ2. We show that any ℒ1-regular finitely additive measure on the algebra generated by ℒ1 can be uniquely extended to an ℒ2-regular measure on the algebra generated by ℒ2. The case when ℒ1 is not necessary contained in ℒ2, as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.http://dx.doi.org/10.1155/S0161171292000929 |
| spellingShingle | Jack-Kang Chan Measures on coallocation and normal lattices International Journal of Mathematics and Mathematical Sciences |
| title | Measures on coallocation and normal lattices |
| title_full | Measures on coallocation and normal lattices |
| title_fullStr | Measures on coallocation and normal lattices |
| title_full_unstemmed | Measures on coallocation and normal lattices |
| title_short | Measures on coallocation and normal lattices |
| title_sort | measures on coallocation and normal lattices |
| url | http://dx.doi.org/10.1155/S0161171292000929 |
| work_keys_str_mv | AT jackkangchan measuresoncoallocationandnormallattices |