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Conditional probability on full Łukasiewicz tribes
Soft Computing ( IF 3.1 ) Pub Date : 2020-02-14 , DOI: 10.1007/s00500-020-04762-6
Peter Eliaš , Roman Frič

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.



中文翻译:

Łukasiewicz完整部落的条件概率

我们在升级的概率模型中研究条件概率和随机依赖/独立性的概念,在该模型中,事件的空间由所有可测量函数的完整Łukasiewicz部落建模,从某个可测量空间进入[0,1]。我们的研究基于联合实验的性质和随机通道的概念,该结构等同于两个可测量空间之间的马尔可夫核的概念。使用退化的随机信道的概念,即在两个空间之间不传输随机信息的信道,我们定义了随机实验的不对称独立性。最后,我们定义了完整的sukasiewicz部落的条件概率概念。

更新日期:2020-04-22
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