Construction of Measure from Semialgebra of Sets1

Noboru Endou

Formalized Mathematics (2015)

  • Volume: 23, Issue: 4, page 309-323
  • ISSN: 1426-2630

Abstract

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In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we give a σ-measure as an extension of the measure on a σ-field. We follow [24], [10], and [31].

How to cite

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Noboru Endou. "Construction of Measure from Semialgebra of Sets1." Formalized Mathematics 23.4 (2015): 309-323. <http://eudml.org/doc/276927>.

@article{NoboruEndou2015,
abstract = {In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we give a σ-measure as an extension of the measure on a σ-field. We follow [24], [10], and [31].},
author = {Noboru Endou},
journal = {Formalized Mathematics},
keywords = {measure theory; pre-measure},
language = {eng},
number = {4},
pages = {309-323},
title = {Construction of Measure from Semialgebra of Sets1},
url = {http://eudml.org/doc/276927},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Noboru Endou
TI - Construction of Measure from Semialgebra of Sets1
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 4
SP - 309
EP - 323
AB - In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we give a σ-measure as an extension of the measure on a σ-field. We follow [24], [10], and [31].
LA - eng
KW - measure theory; pre-measure
UR - http://eudml.org/doc/276927
ER -

References

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