Theorems · Theorem · measure theory

MeasureTheory.AEStronglyMeasurable.mono_set

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {f : α → β} {s t : Set α},
  s ⊆ t → MeasureTheory.AEStronglyMeasurable f (μ.restrict t) → MeasureTheory.AEStronglyMeasurable f (μ.restrict s)

Defined in: Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
Cited by: 6 results in Mathlib
Foundations: Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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Cites9

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

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
le_rflproof · cited by 1,558
MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
MeasureTheory.Measure.restrict_monoproof · cited by 33
MeasureTheory.AEStronglyMeasurable.mono_measureproof · cited by 13

Cited by6

Results whose statement or proof uses this declaration.

StronglyMeasurableAtFilter.eventuallyproof · cited by 3
integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
mellin_convergent_iff_normproof · cited by 1
mellin_convergent_top_of_isBigOproof · cited by 1
mellin_convergent_zero_of_isBigOproof · cited by 1
intervalIntegral.continuousAt_parametric_primitive_of_dominatedproof · cited by 0