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Theorems · Theorem · probability

ProbabilityTheory.gaussianReal_map_continuousLinearMap

∀ {μ : ℝ} {v : NNReal} (L : ℝ →L[ℝ] ℝ),
  MeasureTheory.Measure.map (⇑L) (ProbabilityTheory.gaussianReal μ v) =
    ProbabilityTheory.gaussianReal (L μ) ((L 1 ^ 2).toNNReal * v)
Defined in
Mathlib.Probability.Distributions.Gaussian.Real
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Foundations
Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
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DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureContinuousLinearMap · cited by 5352ContinuousLinearMapNNReal · cited by 4310NNRealMeasureTheory.Measure.map · cited by 858Measure.mapContinuousLinearMap.toLinearMap · cited by 528ContinuousLinearMap.toLin…Real.toNNReal · cited by 267Real.toNNRealProbabilityTheory.gaussianReal · cited by 77ProbabilityTheory.gaussia…ProbabilityTheory.gaussianReal_map_linearMap · cited by 3ProbabilityTheory.gaussia…ProbabilityTheory.gaussianRea…CITED BYCITES

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