measure_Ioc — Mathlib

English

The measure of the singleton {a} is the difference between the value of f at a and its left limit at a: μ_f({a}) = f(a) - leftLim f(a).

Русский

Мера множества {a} равна разности f(a) и левой предела f в a: μ_f({a}) = f(a) - leftLim f(a).

LaTeX

$$μ_f({a}) = f(a) - leftLim f(a)$$

Lean4

@[simp]
theorem measure_Ioc (a b : ℝ) : f.measure (Ioc a b) = ofReal (f b - f a) :=
  by
  rw [StieltjesFunction.measure]
  exact f.outer_Ioc a b

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