Theorems · Theorem · measure theory
MeasureTheory.lintegral_count
∀ {α : Type u_1} [inst : MeasurableSpace α] [MeasurableSingletonClass α] (f : α → ENNReal),
∫⁻ (a : α), f a ∂MeasureTheory.Measure.count = ∑' (a : α), f a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 200 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.
- TopologicalSpaceproof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidproof · cited by 12,281
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- tsumstatement and proof · cited by 1,148
- SummationFilterproof · cited by 607
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracproof · cited by 210
- MeasureTheory.Measure.countstatement · cited by 60
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.hasFiniteIntegral_count_iffproof · cited by 1
- ENNReal.count_const_le_le_of_tsum_leproof · cited by 1
- MeasureTheory.hasFiniteIntegral_count_iff_enormproof · cited by 0