Theorems · Theorem · measure theory
MeasureTheory.measure_lt_top_of_subset
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {s t : Set α}, t ⊆ s → μ s ≠ ⊤ → μ t < ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- 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
- lt_of_le_of_ltproof · cited by 432
- Ne.lt_topproof · cited by 161
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.OuterMeasure.monoproof · cited by 36
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_ne_top_of_subsetproof · cited by 15
- MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff'proof · cited by 1
- BoxIntegral.unitPartition.setFinite_indexproof · cited by 0