Given a Radón measure on each of two locally compact Hausdorff spaces we consider three product measures on the product space - the classical product
measure generated by measurable rectangles as in Munroe, the product measure generated by measurable rectangles and nil sets of Bledsoe and Morse, and a Radón product measure obtained by a Riesz Representation Theorem from the product linear functional of Bourbaki.
For the classical product measure we prove a Fubini Theorem for compact sets although we do not know whether compact sets are measurable, a theorem giving necessary and sufficient conditions for open sets to be measurable, and a theorem that every closed СɣϬ is measurable.
We prove that all three product measures agree on compact sets and thus that the Bledsoe-Morse product measure and the Radón product measure agree on open sets.
Finally, we give examples to show that certain results cannot be extended. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/38827 |
| Date | January 1963 |
| Creators | Godfrey, Michael Colin |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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