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Theorems · Theorem · probability

ProbabilityTheory.gaussianReal_apply_eq_integral

∀ (μ : ℝ) {v : NNReal},
  v ≠ 0 →
    ∀ (s : Set ℝ),
      (ProbabilityTheory.gaussianReal μ v) s = ENNReal.ofReal (∫ (x : ℝ) in s, ProbabilityTheory.gaussianPDFReal μ v x)
Defined in
Mathlib.Probability.Distributions.Gaussian.Real
Cited by
2 results in Mathlib
Foundations
Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
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ProbabilityTheory.gaussianReal_map_const_mul · cited by 4ProbabilityTheory.gaussia…ProbabilityTheory.gaussianReal_map_add_const · cited by 3ProbabilityTheory.gaussia…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealMeasureTheory.integral · cited by 1779MeasureTheory.integralMeasureTheory.Measure.restrict · cited by 1646Measure.restrictMeasureTheory.MeasureSpace.volume · cited by 1323MeasureSpace.volumeMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralENNReal.ofReal · cited by 863ENNReal.ofRealMeasureTheory.ae_of_all · cited by 137MeasureTheory.ae_of_allProbabilityTheory.gaussianReal · cited by 77ProbabilityTheory.gaussia…ProbabilityTheory.gaussianPDFReal · cited by 24ProbabilityTheory.gaussia…MeasureTheory.ofReal_integral_eq_lintegral_ofReal · cited by 22MeasureTheory.ofReal_inte…ProbabilityTheory.gaussianRea…CITED BYCITES

Cites20

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Cited by2

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