This paper focuses on the understanding of countable additivity in the axiomatic definition of probability. Through concept decomposition, example verification and theoretical deduction, the core cognition is refined. The results show that the essence of countable additivity is the rule to solve the probability calculation of an infinite number of mutually exclusive events; as one of the three properties of axiomatic probability, it is based on non-negativity and normalization, and is incomplete without it. In the specific case verification process, this paper follows the logic of  "defining event, calculation of a single event's probability, and finding the target probability". The conclusions show that to understand countable additivity, it is necessary to closely follow the four-layer framework of 'essence-theory-application-reality', in order to grasp its core value and application logic.

Ailing Shi. The Countable Additivity in the Axiomatic Definition of Probability. Frontiers in Educational Research (2026), Vol. 9, Issue 1: 1-7. https://doi.org/10.25236/FER.2026.090101.

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