The Nature of Points in Countable Boolean Lattice Measures

1
D.V.S.R. Anil Kumar
D.V.S.R. Anil Kumar
2
Y.V. Seshagiri Rao
Y.V. Seshagiri Rao
3
Y. Narasimhulu
Y. Narasimhulu
1 Nagarjuna University

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This paper describes a class of null sets; point, lattice measure of a point and lattice semi-finite measure were introduced. Here it has been derived a result that in a countable Boolean lattice the lattice measure of any two points are either disjoint or identical also the class of all points in countable Boolean lattice is countable and proved that Any union countable of null partial lattices is null partial lattice, also established that the class of points in countable Boolean lattice is countable. It has been obtained a theorem that if a countable Boolean lattice is pointless if and only if every non empty set in countable Boolean lattice contains countable number of disjoint non-empty sets. Finally it has been observed that some elementary nature of points in a countable Boolean lattice.

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References

  1. D Kumar,J Venkateswara,E Rao,Ravi Kumar (2011). Characterization of Class of Measurable Borel Lattices.
  2. D Kumar,Y Seshagiri Rao,Y Narasimhulu,Sundaranand Venkata,Putcha (2013). Global Journal of Science Frontier Research.
  3. G Birkhoff (1967). Lattice Theory 3rd ed.
  4. Gene De Both (1973). Additive Set Functions On Lattices Of Sets.
  5. Sengupta Chapter1sigmaAlgebras.
  6. G Gratzer (1978). General Lattice Theory.
  7. P R Halmos (1974). Measure Theory.
  8. Pao -Sheng Hus (2000). Characterization of outer measures associated with lattice measures.
  9. Szasz Gabor (1963). Introduction to lattice theory.
  10. J Tanaka (2009). Unknown Title.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Not applicable for this article.

D.V.S.R. Anil Kumar. 2014. \u201cThe Nature of Points in Countable Boolean Lattice Measures\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 14 (GJSFR Volume 14 Issue F1): .

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GJSFR Volume 14 Issue F1
Pg. 15- 21
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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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May 3, 2014

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This paper describes a class of null sets; point, lattice measure of a point and lattice semi-finite measure were introduced. Here it has been derived a result that in a countable Boolean lattice the lattice measure of any two points are either disjoint or identical also the class of all points in countable Boolean lattice is countable and proved that Any union countable of null partial lattices is null partial lattice, also established that the class of points in countable Boolean lattice is countable. It has been obtained a theorem that if a countable Boolean lattice is pointless if and only if every non empty set in countable Boolean lattice contains countable number of disjoint non-empty sets. Finally it has been observed that some elementary nature of points in a countable Boolean lattice.

This paper describes a class of null sets; point, lattice measure of a point and lattice semi-finite measure were introduced. Here it has been derived a result that in a countable Boolean lattice the lattice measure of any two points are either disjoint or identical also the class of all points in countable Boolean lattice is countable and proved that Any union countable of null partial lattices is null partial lattice, also established that the class of points in countable Boolean lattice is countable. It has been obtained a theorem that if a countable Boolean lattice is pointless if and only if every non empty set in countable Boolean lattice contains countable number of disjoint non-empty sets. Finally it has been observed that some elementary nature of points in a countable Boolean lattice.

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The Nature of Points in Countable Boolean Lattice Measures

D.V.S.R. Anil Kumar
D.V.S.R. Anil Kumar Nagarjuna University
Y.V. Seshagiri Rao
Y.V. Seshagiri Rao
Y. Narasimhulu
Y. Narasimhulu

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