toMeasureOfLEZero_real_apply — Mathlib

English

Taking toSignedMeasure respects the zero-trimmed construction: toMeasureOfZeroLE_toSignedMeasure equals -s when appropriate.

Русский

Тождественно toSignedMeasure сохраняет нулевое тримирование: toMeasureOfZeroLE_toSignedMeasure = -s при подходящих условиях.

LaTeX

$$$ (s.toMeasureOfZeroLE Set.univ MeasurableSet.univ hs).toSignedMeasure = -s $$$

Lean4

theorem toMeasureOfLEZero_real_apply (hi : s ≤[i] 0) (hi₁ : MeasurableSet i) (hj₁ : MeasurableSet j) :
    (s.toMeasureOfLEZero i hi₁ hi).real j = -s (i ∩ j) := by
  simp [measureReal_def, toMeasureOfLEZero_apply _ hi hi₁ hj₁]

Похожие утверждения