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.
@article{bwmeta1.element.doi-10_1515_forma-2016-0006,
author = {Noboru Endou},
title = {Product Pre-Measure},
journal = {Formalized Mathematics},
volume = {24},
year = {2016},
pages = {69-79},
zbl = {1343.28001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0006}
}
Noboru Endou. Product Pre-Measure. Formalized Mathematics, Tome 24 (2016) pp. 69-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0006/
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