Theorems · Theorem · measure theory
Set.Finite.measure_zero
∀ {α : Type u_1} {m0 : MeasurableSpace α} {s : Set α},
s.Finite → ∀ (μ : MeasureTheory.Measure α) [MeasureTheory.NullSingletonClass μ], μ s = 0- Cited by
- 9 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Finitestatement and proof · cited by 1,814
- MeasureTheory.NullSingletonClassstatement and proof · cited by 125
- Set.Finite.countableproof · cited by 30
- Set.Countable.measure_zeroproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.mahlerMeasure_mulproof · cited by 5
- MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonposproof · cited by 1
- MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonnegproof · cited by 1
- MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonposproof · cited by 1
- Polynomial.mahlerMeasure_le_sum_norm_coeffproof · cited by 1
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1
- MeasureTheory.integrableOn_Icc_deriv_smul_iff_of_deriv_nonnegproof · cited by 1
- ae_restrict_of_ae_restrict_inter_Iooproof · cited by 0
- Finset.measure_zeroproof · cited by 0