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Theorems · Theorem · measure theory

MeasureTheory.IsProbabilityMeasure.ne_zero

∀ {α : Type u_1} {m0 : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.IsProbabilityMeasure μ], μ ≠ 0
Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.Probability
Cited by
17 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsProbabilityMeasure

Around this declaration

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

ProbabilityTheory.HasGaussianLaw.aemeasurable · cited by 11HasGaussianLaw.aemeasurab…ProbabilityTheory.mgf_pos · cited by 3ProbabilityTheory.mgf_posMeasureTheory.Measure.isProbabilityMeasure_of_map · cited by 2Measure.isProbabilityMeas…ProbabilityTheory.IsGaussianProcess.aemeasurable · cited by 1IsGaussianProcess.aemeasu…MeasureTheory.exists_lintegral_le · cited by 1MeasureTheory.exists_lint…MeasureTheory.measure_le_integral_pos · cited by 0MeasureTheory.measure_le_…MeasureTheory.measure_le_lintegral_pos · cited by 0MeasureTheory.measure_le_…ProbabilityTheory.mgf_dirac · cited by 0ProbabilityTheory.mgf_dir…MeasureTheory.measure_lintegral_le_pos · cited by 0MeasureTheory.measure_lin…MeasureTheory.exists_notMem_null_integral_le · cited by 0MeasureTheory.exists_notM…MeasureTheory.exists_notMem_null_le_integral · cited by 0MeasureTheory.exists_notM…MeasureTheory.exists_notMem_null_le_lintegral · cited by 0MeasureTheory.exists_notM…MeasureTheory.exists_notMem_null_lintegral_le · cited by 0MeasureTheory.exists_notM…MeasureTheory.exists_integral_le · cited by 0MeasureTheory.exists_inte…MeasureTheory.measure_integral_le_pos · cited by 0MeasureTheory.measure_int…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.IsProbabilityMeasure · cited by 392MeasureTheory.IsProbabili…MeasureTheory.IsProbabilityMeasure.measure_univ · cited by 135IsProbabilityMeasure.meas…MeasureTheory.Measure.measure_univ_eq_zero · cited by 26Measure.measure_univ_eq_z…IsProbabilityMeasure.ne_zeroCITED BYCITES

Cites5

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

Cited by17

Results whose statement or proof uses this declaration.