Theorems · Theorem · measure theory
MeasureTheory.Measure.lintegral_join_le
∀ {α : Type u_1} {mα : MeasurableSpace α} (f : α → ENNReal) (m : MeasureTheory.Measure (MeasureTheory.Measure α)),
∫⁻ (x : α), f x ∂m.join ≤ ∫⁻ (μ : MeasureTheory.Measure α), ∫⁻ (x : α), f x ∂μ ∂m- Defined in
- Mathlib.MeasureTheory.Measure.GiryMonad
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 213 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- le_reflproof · cited by 2,061
- Measurableproof · cited by 1,499
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.lintegral_mono_fn'proof · cited by 33
- MeasureTheory.Measure.joinstatement and proof · cited by 26
- MeasureTheory.exists_measurable_le_lintegral_eqproof · cited by 8
- MeasureTheory.Measure.lintegral_joinproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.lintegral_bind_leproof · cited by 1