Products of Radon measures
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, an...
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ndltd-UBC-oai-circle.library.ubc.ca-2429-388272018-01-05T17:49:22Z Products of Radon measures Godfrey, Michael Colin Topology 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 2011-11-07T21:12:34Z 2011-11-07T21:12:34Z 1963 Text Thesis/Dissertation http://hdl.handle.net/2429/38827 eng 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. University of British Columbia |
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NDLTD |
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English |
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NDLTD |
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Topology |
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Topology Godfrey, Michael Colin Products of Radon measures |
description |
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 |
author |
Godfrey, Michael Colin |
author_facet |
Godfrey, Michael Colin |
author_sort |
Godfrey, Michael Colin |
title |
Products of Radon measures |
title_short |
Products of Radon measures |
title_full |
Products of Radon measures |
title_fullStr |
Products of Radon measures |
title_full_unstemmed |
Products of Radon measures |
title_sort |
products of radon measures |
publisher |
University of British Columbia |
publishDate |
2011 |
url |
http://hdl.handle.net/2429/38827 |
work_keys_str_mv |
AT godfreymichaelcolin productsofradonmeasures |
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1718596254361976832 |