Theorems · Theorem · measure theory

MeasureTheory.measureReal_add_apply

∀ {α : Type u_1} {x : MeasurableSpace α} {s : Set α} {μ₁ μ₂ : MeasureTheory.Measure α},
  autoParam (μ₁ s ≠ ⊤) MeasureTheory.measureReal_add_apply._auto_1 →
    autoParam (μ₂ s ≠ ⊤) MeasureTheory.measureReal_add_apply._auto_3 → (μ₁ + μ₂).real s = μ₁.real s + μ₂.real s

Defined in: Mathlib.MeasureTheory.Measure.Real
Cited by: 6 results in Mathlib
Foundations: Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
Realstatement · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Top.topstatement and proof · cited by 9,680
ENNReal.toRealproof · cited by 859
MeasureTheory.Measure.realstatement · cited by 530
ENNReal.toReal_addproof · cited by 22
MeasureTheory.Measure.add_applyproof · cited by 17

Cited by6

Results whose statement or proof uses this declaration.

MeasureTheory.DominatedFinMeasAdditive.add_measureproof · cited by 4
MeasureTheory.Measure.toSignedMeasure_addproof · cited by 2
MeasureTheory.average_add_measureproof · cited by 1
MeasureTheory.weightedSMul_add_measureproof · cited by 1
MeasureTheory.SignedMeasure.norm_le_totalVariationproof · cited by 1
MeasureTheory.SignedMeasure.toJordanDecomposition_eq_of_eq_add_withDensityproof · cited by 0