DOI: 10.1515/forma-2015-0025 degruyter.com/view/j/forma Construction of Measure from Semialgebra

Summary. In our previous article [21], we showed complete additivity as a condition for extension of a measure. However, this condition is 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 [23], [?], and [?]