Linked from

The 15 pages that link to Countable additivity, each with the reason it gives.

• Lebesgue measureRelated: Lebesgue measure preserves total size across countably many disjoint pieces.

• Probability measureBroader topic: It extends finite probability sums to countably many disjoint events.

• Measure theoryRelated: It is the defining additivity rule for measures.

• Probability spaceRelated: It governs probabilities of countably many mutually exclusive events.

• Borel–Cantelli lemmaRelated: It underlies probability measure continuity used in standard proofs.

• Measure spaceRelated: This rule is the defining consistency condition for the size assignment.

• Borel measureRelated: It governs how Borel measures combine sizes across countably many disjoint Borel sets.

• Nonmeasurable setRelated: Countable additivity drives the contradiction in the usual proof that Vitali sets are nonmeasurable.

• Vitali covering theoremRelated: Disjoint selected balls allow their measures to be summed directly.

• Probability axiomsBroader topic: It extends finite additivity to infinite collections of disjoint events.

• Carathéodory's extension theoremRelated: The construction must preserve this defining requirement of a measure.

• Hahn decomposition theoremRelated: Signed measures retain countable additivity across the partition.

• Sard's theoremRelated: It supports measure-zero arguments that decompose critical sets into countably many pieces.

• Boole's inequalityRelated: Partitioning overlapping events into disjoint pieces connects additivity to the inequality.

• Infinite monkey theoremRelated: The proof uses probability rules that remain valid across infinitely many opportunities.