On Bochner-Kolmogorov Theorem
We prove the Bochner-Kolmogorov theorem on the existence of the limit of projective systems of second countable Hausdorff (non-metrizable) spaces with tight probabilities, such that the projection mappings are merely measurable functions. Our direct and transparent approach (using Lusin’s theorem) should be compared with the previous work where the spaces are assumed metrizable and the main idea was to reduce the general context to a regular one via some isomorphisms. The motivation of the revisit of this classical result is an application to the construction of the continuous time fragmentation processes and related branching processes, based on a measurable identification between the space of all fragmentation sizes considered by J. Bertoin and the limit of a projective system of spaces of finite configurations.
KeywordsBochner-Kolmogorov theorem Space of finite configurations Space of fragmentation sizes
AMS classification (2010):60B05 28A33 60A10
This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS–UEFISCDI, project number PN-II-RU-TE-2011-3-0259.
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