Do any probability measure has to be countably additive by definition?

Question

http://mathworld.wolfram.com/ProbabilityMeasure.html

Wolfram mathworld seems to define the prob measure same as a normalized measure.

Are there any generally accepted definition for a prob measure? I saw many authors simply assume that a prob measure is countably additive.

Answer 1

Probability measures are measures with some additional property. Measures are countably additive. Therefore, probability measures are countably additive.