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Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_one

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s : Set α), ∫⁻ (x : α) in s, 1 ∂μ = μ s
Defined in
Mathlib.MeasureTheory.Integral.Lebesgue.Basic
Cited by
17 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum · cited by 5IsAddFundamentalDomain.me…MeasureTheory.IsFundamentalDomain.measure_eq_tsum · cited by 4IsFundamentalDomain.measu…MeasureTheory.measure_add_lintegral_eq · cited by 3MeasureTheory.measure_add…MeasureTheory.measure_mul_lintegral_eq · cited by 3MeasureTheory.measure_mul…MeasureTheory.Measure.rnDeriv_le_one_of_le · cited by 2Measure.rnDeriv_le_one_of…MeasureTheory.IsFundamentalDomain.measure_eq · cited by 1IsFundamentalDomain.measu…MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac · cited by 1IsFundamentalDomain.measu…MeasureTheory.measure_add_measure_eq · cited by 1MeasureTheory.measure_add…MeasureTheory.ae_measure_preimage_add_right_lt_top · cited by 1MeasureTheory.ae_measure_…MeasureTheory.ae_measure_preimage_mul_right_lt_top · cited by 1MeasureTheory.ae_measure_…MeasureTheory.measure_mul_measure_eq · cited by 1MeasureTheory.measure_mul…MeasureTheory.IsAddFundamentalDomain.measure_eq · cited by 1IsAddFundamentalDomain.me…MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top · cited by 1MeasureTheory.ofReal_setI…MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac · cited by 1IsAddFundamentalDomain.me…ProbabilityTheory.Kernel.comp_parallelComp_comp_copy · cited by 0Kernel.comp_parallelComp_…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealone_mul · cited by 2841one_mulMeasureTheory.Measure.restrict · cited by 1646Measure.restrictMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralMeasureTheory.setLIntegral_const · cited by 11MeasureTheory.setLIntegra…MeasureTheory.setLIntegral_oneCITED BYCITES

Cites9

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Cited by17

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