Categorical characterization of probability product measure Product probability measure as invariant morphism

regular conditional probability measure, transition probability. https://m-hiyama.hatenablog.com/entry/20170329/1490772264 If we restrict morphism to product measure, it becomes directed graph.(p x r) (r x q) = p x q.In particular, (p x 1) (1 x q) = p x q.Embedding is right inverse mapping of forgetful functor, but it is not functor.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-07-13
DOI
https://doi.org/10.5281/zenodo.15871837
Primary Topic
Radioactive Decay and Measurement Techniques
Type
article
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0.00
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Categorical characterization of probability product measure Product probability measure as invariant morphism

Zenodo (CERN European Organization for Nuclear Research)
Radioactive Decay and Measurement Techniques
article

Categorical characterization of probability product measure Product probability measure as invariant morphism

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Abstract

regular conditional probability measure, transition probability. https://m-hiyama.hatenablog.com/entry/20170329/1490772264 If we restrict morphism to product measure, it becomes directed graph.(p x r) (r x q) = p x q.In particular, (p x 1) (1 x q) = p x q.Embedding is right inverse mapping of forgetful functor, but it is not functor.

Zenodo (CERN European Organization for Nuclear Research)
Kyoto Sangyo University (JP)
Decent work and economic growth
Openalex Percentile: Top 42%
Radioactive Decay and Measurement Techniques
DOIOpen Access PDFOpenAlex
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Categorical characterization of probability product measure Product probability measure as invariant morphism · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS