eLpNorm'_trim — Mathlib

English

Let hm be a refinement of σ-algebras m ≤ m0. For any strongly measurable f, eLpNorm' of f over μ trimmed by hm equals eLpNorm' over μ.

Русский

Пусть hm задаёт'économie м1≤м0. Для любой сильно измеримой f eLpNorm' на μ, обрезанном hm, равен eLpNorm' на μ.

LaTeX

$$eLpNorm' f q (μ.trim hm) = eLpNorm' f q μ$$

Lean4

theorem eLpNorm'_trim (hm : m ≤ m0) {f : α → ε} (hf : StronglyMeasurable[m] f) :
    eLpNorm' f q (μ.trim hm) = eLpNorm' f q μ := by
  simp_rw [eLpNorm']
  congr 1
  exact lintegral_trim hm (by fun_prop)

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