The Kullback–Leibler Information Function for Infinite Measures
In this paper, we introduce the Kullback–Leibler information function ρ ( ν , μ ) and prove the local large deviation principle for σ-finite measures μ and finitely additive probability measures ν. In particular, the entropy of a continuous probability distribution ν on the real axis is inte...
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MDPI AG
2016-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/12/448 |
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doaj-2fef9aa7b37f43bdadb9d0abe97362a92020-11-24T22:22:40ZengMDPI AGEntropy1099-43002016-12-01181244810.3390/e18120448e18120448The Kullback–Leibler Information Function for Infinite MeasuresVictor Bakhtin0Edvard Sokal1Department of Mathematics, IT and Landscape Architecture, John Paul II Catholic University of Lublin, Konstantynuv Str. 1H, 20-708 Lublin, PolandDepartment of Mechanics and Mathematics, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, BelarusIn this paper, we introduce the Kullback–Leibler information function ρ ( ν , μ ) and prove the local large deviation principle for σ-finite measures μ and finitely additive probability measures ν. In particular, the entropy of a continuous probability distribution ν on the real axis is interpreted as the exponential rate of asymptotics for the Lebesgue measure of the set of those samples that generate empirical measures close to ν in a suitable fine topology.http://www.mdpi.com/1099-4300/18/12/448Kullback–Leibler information functionentropylarge deviation principleempirical measurefine topologyspectral potential |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Victor Bakhtin Edvard Sokal |
| spellingShingle |
Victor Bakhtin Edvard Sokal The Kullback–Leibler Information Function for Infinite Measures Entropy Kullback–Leibler information function entropy large deviation principle empirical measure fine topology spectral potential |
| author_facet |
Victor Bakhtin Edvard Sokal |
| author_sort |
Victor Bakhtin |
| title |
The Kullback–Leibler Information Function for Infinite Measures |
| title_short |
The Kullback–Leibler Information Function for Infinite Measures |
| title_full |
The Kullback–Leibler Information Function for Infinite Measures |
| title_fullStr |
The Kullback–Leibler Information Function for Infinite Measures |
| title_full_unstemmed |
The Kullback–Leibler Information Function for Infinite Measures |
| title_sort |
kullback–leibler information function for infinite measures |
| publisher |
MDPI AG |
| series |
Entropy |
| issn |
1099-4300 |
| publishDate |
2016-12-01 |
| description |
In this paper, we introduce the Kullback–Leibler information function ρ ( ν , μ ) and prove the local large deviation principle for σ-finite measures μ and finitely additive probability measures ν. In particular, the entropy of a continuous probability distribution ν on the real axis is interpreted as the exponential rate of asymptotics for the Lebesgue measure of the set of those samples that generate empirical measures close to ν in a suitable fine topology. |
| topic |
Kullback–Leibler information function entropy large deviation principle empirical measure fine topology spectral potential |
| url |
http://www.mdpi.com/1099-4300/18/12/448 |
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