Theorems · Theorem · measure theory

MeasureTheory.measureReal_add_sdiff

∀ {α : Type u_1} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α},
  MeasurableSet s →
    autoParam (μ s ≠ ⊤) MeasureTheory.measureReal_add_sdiff._auto_1 →
      autoParam (μ t ≠ ⊤) MeasureTheory.measureReal_add_sdiff._auto_3 → μ.real s + μ.real (t \ s) = μ.real (s ∪ t)

Defined in: Mathlib.MeasureTheory.Measure.Real
Cited by: 2 results in Mathlib
Foundations: Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites14

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 and proof · 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
MeasurableSetstatement and proof · cited by 3,075
MeasureTheory.Measure.realstatement and proof · cited by 530
Set.sdiff_subsetproof · cited by 156
Set.union_sdiff_selfproof · cited by 28
Set.disjoint_sdiff_rightproof · cited by 23

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.measureReal_sdiff'proof · cited by 2
MeasureTheory.measureReal_add_diffproof · cited by 0