Theorems · Theorem · measure theory
MeasureTheory.Measure.InnerRegularWRT.exists_subset_lt_add
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p q : Set α → Prop} {U : Set α} {ε : ENNReal},
μ.InnerRegularWRT p q → p ∅ → q U → μ U ≠ ⊤ → ε ≠ 0 → ∃ K ⊆ U, p K ∧ μ U < μ K + ε- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- zero_addproof · cited by 2,366
- eq_or_neproof · cited by 1,117
- pos_iff_ne_zeroproof · cited by 180
- MeasureTheory.measure_emptyproof · cited by 169
- Set.empty_subsetproof · cited by 70
- MeasureTheory.Measure.InnerRegularWRTstatement and proof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.InnerRegularWRT.measurableSet_of_isOpenproof · cited by 2
- MeasurableSet.exists_isCompact_lt_addproof · cited by 2
- MeasurableSet.exists_isClosed_lt_addproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.weaklyRegular_of_finiteproof · cited by 1