Theorems · Theorem · measure theory
BoundedContinuousFunction.lintegral_lt_top_of_nnreal
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] (μ : MeasureTheory.Measure X)
[MeasureTheory.IsFiniteMeasure μ] (f : BoundedContinuousFunction X NNReal), ∫⁻ (x : X), ↑(f x) ∂μ < ⊤- Cited by
- 11 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- 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
- Top.topstatement · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- ENNReal.ofNNRealstatement · cited by 1,279
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- BoundedContinuousFunctionstatement and proof · cited by 511
- NNDist.nndistproof · cited by 235
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.testAgainstNN_coe_eqproof · cited by 5
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendstoproof · cited by 3
- MeasureTheory.FiniteMeasure.tendsto_of_forall_integral_tendstoproof · cited by 3
- MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_filter_of_le_constproof · cited by 1
- MeasureTheory.FiniteMeasure.injective_toWeakDualBCNNproof · cited by 1
- MeasureTheory.ext_of_forall_integral_eq_of_IsFiniteMeasureproof · cited by 1
- MeasureTheory.FiniteMeasure.limsup_measure_closed_le_of_tendstoproof · cited by 1
- BoundedContinuousFunction.integrable_of_nnrealproof · cited by 0
- MeasureTheory.FiniteMeasure.ext_of_forall_integral_eqproof · cited by 0
- BoundedContinuousFunction.lintegral_of_real_lt_topproof · cited by 0