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Theorems · Theorem · measure theory

MeasureTheory.restrict_withDensity

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
  MeasurableSet s → ∀ (f : α → ENNReal), (μ.withDensity f).restrict s = (μ.restrict s).withDensity f
Defined in
Mathlib.MeasureTheory.Measure.WithDensity
Cited by
15 results in Mathlib
Foundations
Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.withDensity_mul₀ · cited by 5MeasureTheory.withDensity…MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable₀ · cited by 4MeasureTheory.setLIntegra…setIntegral_withDensity_eq_setIntegral_smul₀ · cited by 4setIntegral_withDensity_e…setIntegral_withDensity_eq_setIntegral_toReal_smul₀ · cited by 3setIntegral_withDensity_e…MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar · cited by 3MeasureTheory.restrict_ma…MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smul · cited by 2MeasureTheory.integrableO…Polynomial.Chebyshev.integrable_measureT · cited by 2Chebyshev.integrable_meas…MeasureTheory.setLIntegral_withDensity_eq_lintegral_mul₀' · cited by 1MeasureTheory.setLIntegra…MeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul · cited by 1MeasureTheory.setLIntegra…MeasureTheory.Measure.rnDeriv_restrict · cited by 1Measure.rnDeriv_restrictPolynomial.Chebyshev.integral_measureT · cited by 1Chebyshev.integral_measur…MeasureTheory.Measure.singularPart_restrict · cited by 1Measure.singularPart_rest…MeasureTheory.Measure.rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular · cited by 1Measure.rnDeriv_add_right…MeasureTheory.Measure.withDensity_sub · cited by 0Measure.withDensity_subMeasureTheory.setLIntegral_withDensity_eq_setLIntegral_mul_non_measurable · cited by 0MeasureTheory.setLIntegra…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasurableSet · cited by 3075MeasurableSetMeasureTheory.Measure.restrict · cited by 1646Measure.restrictMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralMeasureTheory.Measure.ext · cited by 308Measure.extMeasureTheory.Measure.withDensity · cited by 265Measure.withDensityMeasurableSet.inter · cited by 167MeasurableSet.interMeasureTheory.Measure.restrict_apply · cited by 159Measure.restrict_applyMeasureTheory.withDensity_apply · cited by 73MeasureTheory.withDensity…MeasureTheory.Measure.restrict_restrict · cited by 38Measure.restrict_restrictMeasureTheory.restrict_withDe…CITED BYCITES

Cites14

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Cited by15

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