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a2ee19a | 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 | import Mathlib
import OAI.Probability.Perceptron.Interpolation.TiltReplicaCoordinate
namespace OAI
noncomputable section
open MeasureTheory ProbabilityTheory Filter Set
open scoped ENNReal NNReal Topology BigOperators BoundedContinuousFunction
namespace SphericalPerceptronFreeEnergy
open Matrix
open scoped InnerProductSpace
variable {H : Type*} [SeminormedAddCommGroup H] [InnerProductSpace ℝ H]
lemma stablePoissonTotal_log_memLp_two {b : ℝ} (hb0 : 0 < b) (hb1 : b < 1) :
MemLp (fun η => Real.log (stablePoissonTotal η)) 2
(poissonRandomMeasureLaw (stableLogIntensity b)) := by
apply (memLp_two_iff_integrable_sq stablePoissonTotal_measurable.log.aestronglyMeasurable).mpr
simpa only [Real.rpow_zero,one_mul] using
stablePoissonTotal_weighted_log_sq_integrable (a := 0) hb0 hb1 hb0
end SphericalPerceptronFreeEnergy
end
end OAI
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