DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How 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.

Finite-alphabet IID source

Definition

Let $A$ be a nonempty finite alphabet identified with $[m]$ , and let $p$ be a probability vector in the sense of Finite distributions, entropy, divergence, and stochastic matrices. A finite-alphabet IID source consists of random elements $X_{i} : (Ω, F, P) \to A$ , $i \geq 1$ , on one probability space, which are independent and identically distributed in the sense of Identical distribution and IID families and have common law $p$ . For every $n \geq 1$ , the finite vector $X^{n} = (X_{1}, \dots, X_{n})$ then has probability $P (X^{n} = x^{n}) = p^{n} (x^{n})$ for each $x^{n} \in A^{n}$ , with $p^{n}$ as in Self-information and surprisal variance for a finite law.

Depends on

Used by

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

Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, 2nd ed., Chapter 3 (standard reference, not scraped)
MIT OpenCourseWare 6.441 Information Theory, Spring 2010, Lecture 3 (standard reference, not scraped)