We consider integral representations of Feller probability kernels from a Tikhonov space X into a Hausdorff space Y by continuous functions from X into Y. From the existence of such a representation for every kernel it follows that the space X has to be 0-dimensional. Moreover, both types of representations coincide in the metrizable case when in addition X is compact and Y is complete. It is also proved that the representation of a single kernel is equivalent to the existence of some non-direct product measure on the product space .
@article{bwmeta1.element.bwnjournal-article-apmv56z1p93bwm,
author = {R. R\k ebowski},
title = {A note on integral representation of Feller kernels},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {93-96},
zbl = {0741.60073},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv56z1p93bwm}
}
R. Rębowski. A note on integral representation of Feller kernels. Annales Polonici Mathematici, Tome 55 (1991) pp. 93-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z1p93bwm/
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