| import OAI.Probability.InvariantIsing.Spectral.EmpiricalSpectralLaw | |
| namespace OAI | |
| /-! Every finite empirical field law has all real-valued moments. -/ | |
| noncomputable section | |
| open MeasureTheory | |
| namespace InvariantIsing | |
| lemma empiricalField_integrable {N : ℕ} (hN : 0 < N) (c : Fin N → ℝ) (f : ℝ → ℝ) : | |
| Integrable f (empiricalSpectralLaw hN c : Measure ℝ) := by | |
| change Integrable f (Measure.sum (fun i : Fin N => ENNReal.ofReal ((1 : ℝ)/N) • Measure.dirac (c i))) | |
| rw [Measure.sum_fintype] | |
| apply integrable_finsetSum_measure.mpr | |
| intro i _ | |
| exact (integrable_dirac (by simp)).smul_measure (by finiteness) | |
| end InvariantIsing | |
| end | |
| end OAI | |