Measures on product spaces and the existence of strong Baire liftings |
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Authors: | S. Grekas C. Gryllakis |
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Affiliation: | (1) Zografou, Box 64075, 15710 Athens, Greece |
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Abstract: | Some notions are introduced for studying measures on product spaces, the main concept being that of property (*). In case when the topological factors are separable metric spaces, this property is equivalent to the completion regularity. We prove that (*) is preserved under arbitrary products of measure spaces. As a consequence, we deduce a series of related results in measure theory (some of which are known). In particular, the following extension of a result by Losert is obtained: Subject to CH, every product of 2 many completion regular measures, each supported on any product of 1 many compact metric spaces admits a strong Baire lifting. |
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