measure_stieltjesFunction_Iic — Mathlib

English

For f ∈ IsMeasurableRatCDF, the Stieltjes function is measurable and its measure on Iic x equals ENNReal.ofReal of its value.

Русский

Для f ∈ IsMeasurableRatCDF функциями Стилтьджеса измеримы, а мера на Iic x равна ENNReal.ofReal от значения функции.

LaTeX

$$measure_stieltjesFunction_Iic$$

Lean4

theorem measure_stieltjesFunction_Iic (a : α) (x : ℝ) :
    (hf.stieltjesFunction a).measure (Iic x) = ENNReal.ofReal (hf.stieltjesFunction a x) :=
  by
  rw [← sub_zero (hf.stieltjesFunction a x)]
  exact (hf.stieltjesFunction a).measure_Iic (tendsto_stieltjesFunction_atBot hf a) _

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