Lax Lean Archive

While this submission is a draft, it cannot be used by other submissions.

Finite amplified-test averaging

Lax342547.AmplifiedTests · concepts/Lax342547/AmplifiedTests.lean · lax-342547

proven

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    Lemma

    Finite Fubini transfers a pointwise amplified-test upper bound to an exception bound for arbitrary whole-unit predicates.

    Concept map
    14 concepts; 7 descendants hidden
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 amplified_bad_mass proven

    2 test_fubini proven

    Lean source view on GitHub

    1import Lax342547.FiniteSampling
    2
    3/-!
    4---
    5title: Finite amplified-test averaging
    6type: lemma
    7---
    8Finite Fubini transfers a pointwise amplified-test upper bound to an exception bound for arbitrary whole-unit predicates.
    9-/
    10
    11namespace Lax342547.AmplifiedTests
    12
    13open Lax342547.MomentSpace Lax342547.RelativeEntropy Lax342547.RetainedImages Lax342547.FiniteSampling
    14open scoped BigOperators
    15
    16axiom test_fubini {A B : Type} [Fintype A] [Fintype B]
    17 (α : A → ℝ) (β : B → ℝ) (T : A → B → Prop) :
    18 (∑ b,β b*cellMass α (fun a => T a b)) =
    19 ∑ a,α a*cellMass β (T a)
    20
    21axiom amplified_bad_mass {A B : Type} [Fintype A] [Fintype B]
    22 (α : A → ℝ) (β : B → ℝ) (T : A → B → Prop) (bad : B → Prop) (c U : ℝ)
    23 (hα : Probability α) (hβ : ∀ b,0 ≤ β b) (hc : 0 < c)
    24 (hlower : ∀ b,bad b → c ≤ cellMass α (fun a => T a b))
    25 (hupper : ∀ a,cellMass β (T a) ≤ U) : cellMass β bad ≤ U/c
    26
    27end Lax342547.AmplifiedTests
    28
    Show ProofShow Proof
    Builds on
    Used by
    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…