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9b6e014 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | 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
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