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.
Strong law does not assert a rate
Remarks
The conclusion of Kolmogorov iid l1 strong law is almost-sure convergence of sample means. It specifies no numerical rate of decay of the error. The finite-variance logarithmic-rate theorem requires an additional second-moment assumption; neither that assumption nor a law of the iterated logarithm is implicit in the law.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- Durrett, §§2.4–2.5, pp. 76–87 (standard reference, not scraped)