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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
Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.Probability
Cited by
11 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsZeroOrProbabilityMeasure

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ProbabilityTheory.integrable_toReal_condDistrib · cited by 2ProbabilityTheory.integra…MeasureTheory.tendsto_integral_meas_thickening_le · cited by 1MeasureTheory.tendsto_int…MeasureTheory.measureReal_le_one · cited by 1MeasureTheory.measureReal…ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure · cited by 1ProbabilityTheory.exists_…ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul · cited by 1Fernique.lintegral_exp_mu…ProbabilityTheory.uniformOn_eq_one_of · cited by 1ProbabilityTheory.uniform…MeasureTheory.levyProkhorovEDist_le_of_forall_le · cited by 1MeasureTheory.levyProkhor…ProbabilityTheory.sum_prob_mem_Ioc_le · cited by 1ProbabilityTheory.sum_pro…ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self · cited by 1ProbabilityTheory.lintegr…MeasureTheory.one_le_prob_iff · cited by 1MeasureTheory.one_le_prob…MeasureTheory.prob_compl_lt_one_sub_of_lt_prob · cited by 0MeasureTheory.prob_compl_…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.univ · cited by 3945Set.univLE.le.trans · cited by 3151le.transMeasureTheory.measure_mono · cited by 338MeasureTheory.measure_monoSet.subset_univ · cited by 228Set.subset_univMeasureTheory.IsZeroOrProbabilityMeasure · cited by 46MeasureTheory.IsZeroOrPro…MeasureTheory.IsZeroOrProbabilityMeasure.measure_univ · cited by 4IsZeroOrProbabilityMeasur…MeasureTheory.prob_le_oneCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.