Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: pre-measure

Sortuj według:

Ogranicz wyniki do:

Product Pre-Measure

100%

Endou N.

Formalized Mathematics

2016

tom 24

nr 1

69-79

In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.

Construction of Measure from Semialgebra of Sets1

100%

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].

Ograniczanie wyników

2 Formalized Mathematics

2 Endou N.

1 2016

1 2015

Wyniki wyszukiwania

Product Pre-Measure

Construction of Measure from Semialgebra of Sets1