Theorems · Theorem · measure theory
MeasureTheory.measureReal_biUnion_finset_le
∀ {α : Type u_1} {β : Type u_2} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s : Finset β) (f : β → Set α),
μ.real (⋃ b ∈ s, f b) ≤ ∑ p ∈ s, μ.real (f p)- Defined in
- Mathlib.MeasureTheory.Measure.Real
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Set.iUnionstatement and proof · cited by 2,483
- le_reflproof · cited by 2,061
- add_le_addproof · cited by 666
- MeasureTheory.Measure.realstatement and proof · cited by 530
- Set.iUnion_congr_Propproof · cited by 374
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.measureReal_iUnion_fintype_leproof · cited by 0