Theorems · Theorem · measure theory
MeasureTheory.prob_le_one
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsZeroOrProbabilityMeasure μ]
{s : Set α}, μ s ≤ 1- Cited by
- 11 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- 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.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- MeasureTheory.measure_monoproof · cited by 338
- Set.subset_univproof · cited by 228
- MeasureTheory.IsZeroOrProbabilityMeasurestatement and proof · cited by 46
- MeasureTheory.IsZeroOrProbabilityMeasure.measure_univproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integrable_toReal_condDistribproof · cited by 2
- MeasureTheory.tendsto_integral_meas_thickening_leproof · cited by 1
- MeasureTheory.measureReal_le_oneproof · cited by 1
- ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1
- ProbabilityTheory.uniformOn_eq_one_ofproof · cited by 1
- MeasureTheory.levyProkhorovEDist_le_of_forall_leproof · cited by 1
- ProbabilityTheory.sum_prob_mem_Ioc_leproof · cited by 1
- ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_selfproof · cited by 1
- MeasureTheory.one_le_prob_iffproof · cited by 1
- MeasureTheory.prob_compl_lt_one_sub_of_lt_probproof · cited by 0