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.
State-space and index-set boundaries of the two extension routes
Under countable choice and dependent choice, the countable theorem Assuming countable and dependent choice, countable products of arbitrary probability spaces covers arbitrary measurable coordinate spaces but only product finite marginals. The arbitrary-index theorem Assuming the Axiom of Choice, Kolmogorov extension for arbitrary families of standard Borel coordinate spaces covers general consistent finite-dimensional laws, but requires standard-Borel coordinates and AC in the compact-product route. Recursive kernel constructions require extra conditional-probability data and belong to the later Markov-kernel page.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
16 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
- Kajino, Probability Theory, Theorem 3.65 (standard reference, not scraped)
- Shalizi, Building Processes, Theorem 29 (standard reference, not scraped)