Theorems · Theorem · measure theory

MeasureTheory.MemLp.condExp

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {E : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {f : α → E} {p : ENNReal},
  1 ≤ p → MeasureTheory.MemLp f p μ → MeasureTheory.MemLp μ[f | m] p μ

Defined in: Mathlib.MeasureTheory.Function.ConditionalExpectation.Real
Cited by: 3 results in Mathlib
Foundations: Depth 310 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace CompleteSpace

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Cites34

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

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Top.topproof · cited by 9,680
Norm.normproof · cited by 5,413
CompleteSpacestatement and proof · cited by 2,532
MeasureTheory.aeproof · cited by 2,352
Filter.univ_mem'proof · cited by 1,672
LT.lt.neproof · cited by 872

Cited by3

Results whose statement or proof uses this declaration.

ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExpproof · cited by 3
MeasureTheory.eLpNorm_condExp_le_eLpNormproof · cited by 3
ProbabilityTheory.integral_condVar_add_variance_condExpproof · cited by 0