Theorems · Theorem · measure theory
MeasureTheory.Measure.notMem_support_iff_exists
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] {μ : MeasureTheory.Measure X} {x : X},
x ∉ μ.support ↔ ∃ U ∈ nhds x, μ U = 0A point x lies outside the support of μ iff some neighborhood of x has measure zero.
- Defined in
- Mathlib.MeasureTheory.Measure.Support
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- MeasureTheory.Measure.supportstatement · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.subset_compl_support_of_isOpenproof · cited by 1
- MeasureTheory.Measure.support_mem_ae_of_isLindelofproof · cited by 1
- MeasureTheory.Measure.measure_eq_zero_of_isCompact_subset_compl_supportproof · cited by 1