Summary
The problem of limits of directed projective systems of probability spaces is treated from the categorical point of view, with certain equivalence classes of measurable measurepreserving mappings, or of regular conditional probabilities playing the role of morphisms. A. o. the existence of limits of such systems is established under the condition that the spaces carry compact generating pavings, without invoking conditions like Bochners' sequential maximality. There are some side results on liftings and general martingales.
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This research was supported in part by a grant from the National Research Council of Canada.
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Scheffer, C.L. Limits of directed projective systems of probability spaces. Z. Wahrscheinlichkeitstheorie verw Gebiete 13, 60–80 (1969). https://doi.org/10.1007/BF00535797
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DOI: https://doi.org/10.1007/BF00535797