projectiveFamilyContent_ne_top — Mathlib

English

If every P J is finite, then the content is never infinite: projectiveFamilyContent hP s ≠ ∞.

Русский

Если всякий P J конечна по мере, то содержимое не бесконечно: projectiveFamilyContent hP s ≠ ∞.

LaTeX

$$[∀ J, IsFiniteMeasure (P J)] ⇒ projectiveFamilyContent hP s ≠ ∞$$

Lean4

theorem projectiveFamilyContent_ne_top [∀ J, IsFiniteMeasure (P J)] (hP : IsProjectiveMeasureFamily P) :
    projectiveFamilyContent hP s ≠ ∞ :=
  by
  rw [projectiveFamilyContent_eq hP, projectiveFamilyFun]
  split_ifs with hs
  · exact measure_ne_top _ _
  · exact ENNReal.zero_ne_top

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