measure_Iic — Mathlib

English

If f tends to l at −∞, then the measure of the left-open interval Iio(x) is infinite: μ_f(Iio(x)) = ∞.

Русский

Если f стремится к l при −∞, то мера Iio(x) бесконечна: μ_f(Iio(x)) = ∞.

LaTeX

$$μ_f(Iio(x)) = \infty$$

Lean4

theorem measure_Iic {l : ℝ} (hf : Tendsto f atBot (𝓝 l)) (x : ℝ) : f.measure (Iic x) = ofReal (f x - l) :=
  by
  refine tendsto_nhds_unique (tendsto_measure_Ioc_atBot _ _) ?_
  simp_rw [measure_Ioc]
  exact ENNReal.tendsto_ofReal (Tendsto.const_sub _ hf)

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