一个测度的象和互反象。相容性定理
Image and Reciprocal Image of a Measure. Compatibility Theorem
摘要：
本文提出在通常的概率论基础上，增加三个定义和一个新定理，从而取代了通常赋予条件概率概念的中心地位。当在两个可测空间之间定义映射$ϕ$时，对于在第一空间上引入的每个测度$μ$，对应于第二空间上的图像$ϕ[μ]$，并且，对于在第二空间上定义的每个测度$ν$，对应于第一空间上的互逆图像$ϕ^{-1}[ν]$。由于两个测度的交集$\cap$很容易引入，因此像$ ϕ[ μ\cap ϕ^{-1} [ν] ] = ϕ[μ] \cap ν$这样的关系是有意义的。这的确是理论的一个定理。这个定理使从物理测量中得出的推论具有数学上的一致性。
英文摘要：
It 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.
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