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Conditional probability on full Łukasiewicz tribes

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Abstract

We study notions of conditional probability and stochastic dependence/independence in an upgraded probability model in which the space of events is modeled by a full Łukasiewicz tribe of all measurable functions from some measurable space into [0, 1]. Our study is based on properties of joint experiments and the notion of stochastic channel, a construct equivalent to the notion of Markov kernel between two measurable spaces. Using the notion of a degenerated stochastic channel, a channel transmitting no stochastic information between two spaces, we define an asymmetrical independence of random experiments. Finally, we define the notion of conditional probability on full Łukasiewicz tribes.

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Acknowledgements

First author gratefully acknowledge the support by the grant of the Slovak Scientific Grant Agency VEGA No. 2/0097/20. Second author gratefully acknowledge the support by the Grant of the Slovak Research and Development Agency under contract APVV-16-0073.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Peter Eliaš & Roman Frič

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  1. Peter Eliaš
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  2. Roman Frič
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Correspondence to Peter Eliaš.

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Communicated by A. Di Nola.

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Eliaš, P., Frič, R. Conditional probability on full Łukasiewicz tribes. Soft Comput 24, 6521–6529 (2020). https://doi.org/10.1007/s00500-020-04762-6

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