Theorems · Theorem · measure theory
MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint
∀ {α : Type u_1} {ι : Type u_8} {x : MeasurableSpace α} (μ : MeasureTheory.Measure α) {As : ι → Set α},
(∀ (i : ι), MeasurableSet (As i)) → Pairwise (Function.onFun Disjoint As) → ∑' (i : ι), μ (As i) ≤ μ (⋃ i, As i)The measure of a disjoint union (even uncountable) of measurable sets is at least the sum of the measures of the sets.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- Set.iUnionstatement · cited by 2,483
- Disjointstatement and proof · cited by 2,201
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePosproof · cited by 1
- Set.Infinite.meas_eq_topproof · cited by 0