case h
Ω : Type u_1
inst✝ : Nonempty Ω
m0 : MeasurableSpace Ω
μ : FiniteMeasure Ω
⊢ ∀ (s : Set Ω),
    MeasurableSet s →
      (fun s => ENNReal.toNNReal (↑↑↑μ s)) s =
        (fun s => ENNReal.toNNReal (↑↑↑(mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)) s)) s
Ω : Type u_1
inst✝ : Nonempty Ω
m0 : MeasurableSpace Ω
μ : FiniteMeasure Ω
⊢ μ = mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)
apply eq_of_forall_apply_eq
case h
Ω : Type u_1
inst✝ : Nonempty Ω
m0 : MeasurableSpace Ω
μ : FiniteMeasure Ω
s : Set Ω
_s_mble : MeasurableSet s
⊢ (fun s => ENNReal.toNNReal (↑↑↑μ s)) s =
    (fun s => ENNReal.toNNReal (↑↑↑(mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)) s)) s
case h
Ω : Type u_1
inst✝ : Nonempty Ω
m0 : MeasurableSpace Ω
μ : FiniteMeasure Ω
⊢ ∀ (s : Set Ω),
    MeasurableSet s →
      (fun s => ENNReal.toNNReal (↑↑↑μ s)) s =
        (fun s => ENNReal.toNNReal (↑↑↑(mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)) s)) s
intro s _s_mble
no goals
case h
Ω : Type u_1
inst✝ : Nonempty Ω
m0 : MeasurableSpace Ω
μ : FiniteMeasure Ω
s : Set Ω
_s_mble : MeasurableSet s
⊢ (fun s => ENNReal.toNNReal (↑↑↑μ s)) s =
    (fun s => ENNReal.toNNReal (↑↑↑(mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)) s)) s
rw [μ.self_eq_mass_mul_normalize s, coeFn_smul_apply, smul_eq_mul,
  ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn]