Image and Reciprocal Image of a Measure. Compatibility Theorem

dc.creatorTarantola, Albert
dc.date2008-10-27
dc.date2008-11-04
dc.date.accessioned2026-07-07T10:15:10Z
dc.date.available2026-07-07T10:15:10Z
dc.descriptionIt is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $ϕ$ is defined between two measurable spaces, to each measure $μ$ introduced on the first space, there corresponds an image $ϕ[μ]$ on the second space, and, reciprocally, to each measure $ν$ defined on the second space the corresponds a reciprocal image $ϕ^{-1}[ν]$ on the first space. As the intersection $\cap$ of two measures is easy to introduce, a relation like $ ϕ[ μ\cap ϕ^{-1} [ν] ] = ϕ[μ] \cap ν$ makes sense. It is, indeed, a theorem of the theory. This theorem gives mathematical consistency to inferences drawn from physical measurements.
dc.description19 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/0810.4749
dc.identifierhttp://arxiv.org/abs/0810.4749
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173091
dc.subjectProbability
dc.titleImage and Reciprocal Image of a Measure. Compatibility Theorem
dc.typetext

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