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Construction of Measure from Semialgebra of Sets1

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Endou N.

Formalized Mathematics

2015

tom 23

nr 4

309-323

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].

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1 Formalized Mathematics

1 Endou N.

1 2015

Wyniki wyszukiwania

Construction of Measure from Semialgebra of Sets1