Theorems · Theorem · measure theory
LowerSemicontinuous.measurable
∀ {α : Type u_1} {δ : Type u_4} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
{mδ : MeasurableSpace δ} [inst_2 : LinearOrder α] [OrderTopology α] [SecondCountableTopology α]
[inst : TopologicalSpace δ] [OpensMeasurableSpace δ] {f : δ → α}, LowerSemicontinuous f → Measurable f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MeasurableSpacestatement and proof · cited by 13,106
- LinearOrderstatement and proof · cited by 8,572
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement · cited by 1,499
- OrderTopologystatement and proof · cited by 1,355
- SecondCountableTopologystatement and proof · cited by 750
- OpensMeasurableSpacestatement and proof · cited by 636
- IsOpen.measurableSetproof · cited by 82
- LowerSemicontinuousstatement and proof · cited by 69
- measurable_of_Ioiproof · cited by 4
- LowerSemicontinuous.isOpen_preimageproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_le_lowerSemicontinuous_lintegral_geproof · cited by 2
- MeasureTheory.exists_lt_lowerSemicontinuous_lintegral_ge_of_aemeasurableproof · cited by 1
- MeasureTheory.exists_lt_lowerSemicontinuous_integral_gt_nnrealproof · cited by 1
- MeasureTheory.SimpleFunc.exists_le_lowerSemicontinuous_lintegral_geproof · cited by 1