Theorems · Theorem · measure theory
Antitone.locallyIntegrable
∀ {X : Type u_1} {E : Type u_6} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : NormedAddCommGroup E]
{μ : MeasureTheory.Measure X} [BorelSpace X] [inst_4 : ConditionallyCompleteLinearOrder X]
[inst_5 : ConditionallyCompleteLinearOrder E] [OrderTopology X] [OrderTopology E] [SecondCountableTopology E]
{f : X → E} [MeasureTheory.IsLocallyFiniteMeasure μ], Antitone f → MeasureTheory.LocallyIntegrable f μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- BorelSpacestatement and proof · cited by 1,602
- OrderTopologystatement and proof · cited by 1,355
- SecondCountableTopologystatement and proof · cited by 750
- Antitonestatement and proof · cited by 563
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- MeasureTheory.LocallyIntegrablestatement · cited by 90
- Antitone.dual_rightproof · cited by 42
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.