Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Agreement with the published finite probability-space definition
The earlier item Finite probability spaces, outcome weights, events, and event probabilities and the present measure-theoretic formulation describe the same finite object. The theorem above does not replace the published finite definition; it identifies it with the probability-measure language on the full power set.
This agreement keeps two boundary features visible. First, every subset of a finite sample space remains measurable. Second, an outcome of weight is still part of the sample space, so a nonempty event may still have probability .
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Rick Durrett, Probability: Theory and Examples, 5th ed., Section 1.1 (standard reference, not scraped)