| import Mathlib | |
| import OAI.Analysis.BrownMeasure.Determinant | |
| import OAI.Analysis.BrownMeasure.Dirac | |
| import OAI.Analysis.BrownMeasure.Orbit | |
| import OAI.Analysis.BrownMeasure.Resolvent | |
| import OAI.Analysis.FiniteFactor.Main | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory | |
| namespace FiniteFactor | |
| theorem productBrown : ProductBrownClaim := by | |
| intro θ hθ | |
| refine ⟨inferInstance, dirac_zero_support_compact, ?_⟩ | |
| intro z | |
| rw [expLogPotential_dirac_zero] | |
| by_cases hz : z = 0 | |
| · subst z | |
| simp only [map_zero, sub_zero, norm_zero, ENNReal.ofReal_zero] | |
| exact sourceOperator_determinant_zero θ hθ | |
| · exact sourceResolvent_determinant θ hθ hz | |
| end FiniteFactor | |
| end | |
| end OAI | |