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Theorems · Theorem · measure theory

MeasureTheory.dominatedFinMeasAdditive_weightedSMul

∀ {α : Type u_1} {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {x : MeasurableSpace α}
  (μ : MeasureTheory.Measure α), MeasureTheory.DominatedFinMeasAdditive μ (MeasureTheory.weightedSMul μ) 1
Defined in
Mathlib.MeasureTheory.Integral.Bochner.L1
Cited by
35 results in Mathlib
Foundations
Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace

Around this declaration

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

MeasureTheory.integral_congr_ae · cited by 110MeasureTheory.integral_co…MeasureTheory.integral_const · cited by 75MeasureTheory.integral_co…MeasureTheory.integral_zero · cited by 59MeasureTheory.integral_ze…MeasureTheory.integral_undef · cited by 58MeasureTheory.integral_un…MeasureTheory.integral_sub · cited by 55MeasureTheory.integral_subMeasureTheory.integral_zero_measure · cited by 50MeasureTheory.integral_ze…MeasureTheory.integral_add · cited by 49MeasureTheory.integral_addMeasureTheory.integral_eq_setToFun · cited by 31MeasureTheory.integral_eq…MeasureTheory.integral_neg · cited by 30MeasureTheory.integral_negMeasureTheory.integral_smul · cited by 23MeasureTheory.integral_sm…MeasureTheory.integral_smul_measure · cited by 22MeasureTheory.integral_sm…MeasureTheory.integral_nonneg_of_ae · cited by 17MeasureTheory.integral_no…MeasureTheory.integral_finsetSum · cited by 13MeasureTheory.integral_fi…MeasureTheory.tendsto_integral_filter_of_dominated_convergence · cited by 10MeasureTheory.tendsto_int…MeasureTheory.enorm_integral_le_lintegral_enorm · cited by 8MeasureTheory.enorm_integ…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNormedSpace · cited by 12499NormedSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureTop.top · cited by 9680Top.topContinuousLinearMap · cited by 5352ContinuousLinearMapLE.le.trans · cited by 3151le.transMeasurableSet · cited by 3075MeasurableSetone_mul · cited by 2841one_mulEq.le · cited by 605Eq.leMeasureTheory.Measure.real · cited by 530Measure.realMeasureTheory.dominatedFinMea…CITED BYCITES

Cites19

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Cited by35

Results whose statement or proof uses this declaration.