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Hopefully fixed all the lean errors
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teorth committed Nov 16, 2023
1 parent 7d59504 commit f60977e
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4 changes: 3 additions & 1 deletion PFR/entropy_pfr.lean
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@@ -1,7 +1,7 @@
import PFR.entropy_basic
import PFR.f2_vec
import PFR.ruzsa_distance
import PFR.tau-functional
import PFR.tau_functional

/-!
# Entropic version of polynomial Freiman-Ruzsa conjecture
Expand All @@ -14,6 +14,8 @@ Here we prove the entropic version of the polynomial Freiman-Ruzsa conjecture.
-/

open MeasureTheory

variable {Ω_0 Ω'_0 : Type*} [mΩ_0 : MeasurableSpace Ω_0] (μ_0 : Measure Ω_0) [mΩ'_0 : MeasurableSpace Ω'_0] (μ'_0 : Measure Ω'_0)

variable {Ω Ω' Ω'' Ω''' : Type*} [mΩ : MeasurableSpace Ω] (μ : Measure Ω) [mΩ' : MeasurableSpace Ω'] (μ' : Measure Ω') [mΩ'' : MeasurableSpace Ω''] (μ'' : Measure Ω'') [mΩ''' : MeasurableSpace Ω'''] (μ''' : Measure Ω''')
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4 changes: 3 additions & 1 deletion PFR/tau_functional.lean
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@@ -1,3 +1,4 @@

import PFR.f2_vec
import PFR.ruzsa_distance

Expand All @@ -7,6 +8,7 @@ import PFR.ruzsa_distance
Definition of the tau functional and basic facts
-/
open MeasureTheory

variable {Ω_0 Ω'_0 : Type*} [mΩ_0 : MeasurableSpace Ω_0] (μ_0 : Measure Ω_0) [mΩ'_0 : MeasurableSpace Ω'_0] (μ'_0 : Measure Ω'_0)

Expand All @@ -17,7 +19,7 @@ variable [AddCommGroup G] [ElementaryAddGroup G 2] [Fintype G]
variable (X_0_1: Ω_0 → G) (X_0_2: Ω'_0 → G)
(X_1: Ω → G) (X_2: Ω' → G)

def eta := (9:ℝ)⁻¹
noncomputable def eta := (9:ℝ)⁻¹

/-- If $X_1,X_2$ are two $G$-valued random variables, then
$$ \tau[X_1; X_2] \coloneqq d[X_1; X_2] + \eta d[X^0_1; X_1] + \eta d[X^0_2; X_2].$$ --/
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