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.

Fisher-information metric distance to a set

Definition

Let $d \geq 1$ and let $I$ be an invertible real symmetric positive-definite $d \times d$ matrix. Define $∥ v ∥_{I} : = \sqrt{v^{T} I v}$ for $v \in R^{d}$ . For a nonempty set $C \subseteq R^{d}$ define

$d_{I} (x, C) : = \inf_{c \in C} ∥ x - c ∥_{I} .$

This is the distance from $x$ to $C$ in the norm induced by $I$ . The definition uses an infimum; attainment is proved separately when a later result requires it.

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Peter Bartlett, Theoretical Statistics, Stat 210B Lecture 26 (standard reference, not scraped)
Steven G. Self and Kung-Yee Liang, Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions (standard reference, not scraped)