| import OAI.Probability.ClassicalON.BondSigns | |
| namespace OAI | |
| universe uV | |
| noncomputable section | |
| open MeasureTheory | |
| open scoped BigOperators ENNReal | |
| namespace ClassicalON | |
| variable {V : Type uV} [Fintype V] | |
| theorem isingReference_singleton (s : V → Bool) : | |
| isingReference {s}=(2 : ℝ≥0∞)⁻¹^Fintype.card V := by | |
| classical | |
| rw [isingReference,Measure.pi_singleton] | |
| simp [signLaw] | |
| open scoped Classical in | |
| theorem integral_isingReference (f : (V → Bool) → ℝ) : | |
| (∫ s,f s ∂isingReference)=(2 : ℝ)⁻¹^Fintype.card V*∑ s,f s := by | |
| classical | |
| rw [integral_fintype (compact_integrable continuous_of_discreteTopology)] | |
| simp only [Measure.real,isingReference_singleton,ENNReal.toReal_pow,ENNReal.toReal_inv, | |
| ENNReal.toReal_ofNat,smul_eq_mul,← Finset.mul_sum] | |
| end ClassicalON | |
| end | |
| end OAI | |