Additive Measure


Definition of finitely additive class
Consider that the family of subsets of space satisfies the following conditions:

Definition of finitely additive measure
The set function defined in the finitely additive class of space satisfies the following conditions:
  1. For ,


Definition of completely additive measure
Consider a finitely additive measure satisfying the following conditions, i.e., the denumerably infinite sets satisfy:

Example

a real monotone increasing function in ( constant)
If we consider for a finite interval , then is a finitely additive measure.
is right-hand continuous, is a completely additive measure.

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