lpMeasToLpTrim — Mathlib

English

Equality a.e. between lpMeasSubgroupToLpTrim f and f holds.

Русский

a.e. равенство между lpMeasSubgroupToLpTrim f и f держится.

LaTeX

$$$lpMeasSubgroupToLpTrim F p μ hm f =ᵐ[μ] f$$$

Lean4

/-- Map from `lpMeas` to `Lp F p (μ.trim hm)`. -/
noncomputable def lpMeasToLpTrim (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) : Lp F p (μ.trim hm) :=
  MemLp.toLp (mem_lpMeas_iff_aestronglyMeasurable.mp f.mem).choose (memLp_trim_of_mem_lpMeasSubgroup hm f.1 f.mem)

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