Operational Statistics. I. Basic Concepts

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Abstract
A generalized notion of a ``sample space'' is developed which allows for the simultaneous representation of the outcomes of a set of related ``random experiments.'' Affiliated with each such generalized sample space is a so‐called ``logic,'' the elements of which are propositions that can be confirmed or refuted by observing the outcomes of the random experiments. Stochastic models for the experimental situation represented by a given sample space are introduced, and it is shown that such stochastic models induce generalized probability measures on the logic of this sample space.

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