Theorems · Theorem · measure theory
MeasureTheory.Content.innerContent_iSup_nat
∀ {G : Type w} [inst : TopologicalSpace G] (μ : MeasureTheory.Content G) [R1Space G] (U : ℕ → TopologicalSpace.Opens G),
μ.innerContent (⨆ i, U i) ≤ ∑' (i : ℕ), μ.innerContent (U i)The inner content of a supremum of opens is at most the sum of the individual inner contents.
- Defined in
- Mathlib.MeasureTheory.Measure.Content
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- SetLike.coeproof · cited by 8,199
- Finset.sumproof · cited by 5,195
- Set.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- le_reflproof · cited by 2,061
- TopologicalSpace.Opensstatement and proof · cited by 2,040
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Content.innerContent_iUnion_natproof · cited by 6
- MeasureTheory.Content.innerContent_pos_of_is_add_left_invariantproof · cited by 1
- MeasureTheory.Content.innerContent_pos_of_is_mul_left_invariantproof · cited by 1