Sections / Section 13: Hierarchical Architecture / welfareDistanceFn

Welfare Distance Fn

defprovedHierarchy

Documentation

Lean 4 Proof

def welfareDistanceFn (z : ℝ) : ℝ := z - 1 - Real.log z

Dependency Graph

Used by

kl_reverse welfareDistanceFn_nonneg levelWelfareLoss hierarchical_kl welfare_eq_bregman aggregateWelfareLoss_eq_zero_iff extendedWelfare diversityWelfareLoss welfareDistanceFn_eq_zero_iff aggregateWelfareLoss lyapunov_within_level_dissipation welfareDistanceFn_pos welfare_eq_kl welfareDistanceFn_at_one welfareDistanceFn_deriv

Location

thesis/CESProofs/Hierarchy/Defs.lean:127

Module Section

Core definitions for the Lean formalization of Paper 4:

In the same file

HierarchicalCESEconomy convergenceSpeed convergenceSpeed_pos ngmEntry ngmEntry_pos cycleProductBeta cycleProductBeta_pos welfareDistanceFn_at_one welfareDistanceFn_nonneg welfareDistanceFn_eq_zero_iff welfareDistanceFn_strictly_convex treeCoefficient institutionalQuality institutionalQuality_pos welfareContribution welfareContribution_nonneg logisticElasticity logisticElasticity_zero logisticElasticity_half logisticElasticity_denom_pos