Theorems · Theorem · measure theory

MeasureTheory.measureReal_sdiff_add_inter

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

Defined in: Mathlib.MeasureTheory.Measure.Real
Cited by: 1 results in Mathlib
Foundations: Depth 190 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
MeasurableSetstatement and proof · cited by 3,075
add_commproof · cited by 1,535
MeasureTheory.Measure.realstatement and proof · cited by 530
MeasureTheory.measureReal_inter_add_sdiffproof · cited by 2

Cited by1

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MeasureTheory.measureReal_diff_add_interproof · cited by 0