It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.
@article{bwmeta1.element.bwnjournal-article-smv101i2p123bwm,
author = {Paolo de Lucia and Pedro Morales},
title = {A noncommutative version of a Theorem of Marczewski for submeasures},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {123-138},
zbl = {0812.28009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p123bwm}
}
de Lucia, Paolo; Morales, Pedro. A noncommutative version of a Theorem of Marczewski for submeasures. Studia Mathematica, Tome 103 (1992) pp. 123-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p123bwm/
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