self_eq_mass_smul_normalize — Mathlib

English

For any f, the map μ ↦ μ.toFiniteMeasure.testAgainstNN f is continuous.

Русский

Для любого f отображение μ ↦ μ.toFiniteMeasure.testAgainstNN f непрерывно.

LaTeX

$$$\\text{continuous_testAgainstNN_eval}(f)$$$

Lean4

theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeasure :=
  by
  apply eq_of_forall_apply_eq
  intro s _s_mble
  rw [μ.self_eq_mass_mul_normalize s, smul_apply, smul_eq_mul, ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn]

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