File: Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean

full_name: Real.measurable_exp
code: @[measurability]
theorem measurable_exp : Measurable exp 
goal: Measurable Real.exp

full_name: Real.measurable_log
code: @[measurability]
theorem measurable_log : Measurable log 
goal: Measurable Real.log

full_name: Real.measurable_of_measurable_exp
code: lemma measurable_of_measurable_exp {α : Type*} {_ : MeasurableSpace α} {f : α → ℝ}
    (hf : Measurable (fun x ↦ exp (f x))) :
    Measurable f 
goal: ∀ {x : MeasurableSpace α} {f : α → ℝ}, (Measurable fun x => Real.exp (f x)) → Measurable f

full_name: Real.aemeasurable_of_aemeasurable_exp
code: lemma aemeasurable_of_aemeasurable_exp {α : Type*} {_ : MeasurableSpace α} {f : α → ℝ}
    {μ : MeasureTheory.Measure α} (hf : AEMeasurable (fun x ↦ exp (f x)) μ) :
    AEMeasurable f μ 
goal: ∀ {x : MeasurableSpace α} {f : α → ℝ} {μ : MeasureTheory.Measure α},
  AEMeasurable (fun x => Real.exp (f x)) μ → AEMeasurable f μ

full_name: Real.measurable_sin
code: @[measurability]
theorem measurable_sin : Measurable sin 
goal: Measurable Real.sin

full_name: Real.measurable_cos
code: @[measurability]
theorem measurable_cos : Measurable cos 
goal: Measurable Real.cos

full_name: Real.measurable_sinh
code: @[measurability]
theorem measurable_sinh : Measurable sinh 
goal: Measurable Real.sinh

full_name: Real.measurable_cosh
code: @[measurability]
theorem measurable_cosh : Measurable cosh 
goal: Measurable Real.cosh

full_name: Real.measurable_arcsin
code: @[measurability]
theorem measurable_arcsin : Measurable arcsin 
goal: Measurable Real.arcsin

full_name: Real.measurable_arccos
code: @[measurability]
theorem measurable_arccos : Measurable arccos 
goal: Measurable Real.arccos

full_name: Complex.measurable_re
code: @[measurability]
theorem measurable_re : Measurable re 
goal: Measurable Complex.re

full_name: Complex.measurable_im
code: @[measurability]
theorem measurable_im : Measurable im 
goal: Measurable Complex.im

full_name: Complex.measurable_ofReal
code: @[measurability]
theorem measurable_ofReal : Measurable ((↑) : ℝ → ℂ) 
goal: Measurable Complex.ofReal'

full_name: Complex.measurable_exp
code: @[measurability]
theorem measurable_exp : Measurable exp 
goal: Measurable Complex.exp

full_name: Complex.measurable_sin
code: @[measurability]
theorem measurable_sin : Measurable sin 
goal: Measurable Complex.sin

full_name: Complex.measurable_cos
code: @[measurability]
theorem measurable_cos : Measurable cos 
goal: Measurable Complex.cos

full_name: Complex.measurable_sinh
code: @[measurability]
theorem measurable_sinh : Measurable sinh 
goal: Measurable Complex.sinh

full_name: Complex.measurable_cosh
code: @[measurability]
theorem measurable_cosh : Measurable cosh 
goal: Measurable Complex.cosh

full_name: Complex.measurable_arg
code: @[measurability]
theorem measurable_arg : Measurable arg 
goal: Measurable Complex.arg

full_name: Complex.measurable_log
code: @[measurability]
theorem measurable_log : Measurable log 
goal: Measurable Complex.log

full_name: Measurable.exp
code: @[measurability]
theorem Measurable.exp : Measurable fun x => Real.exp (f x) 
goal: Measurable fun x => Real.exp (f x)

full_name: Measurable.log
code: @[measurability]
theorem Measurable.log : Measurable fun x => log (f x) 
goal: Measurable fun x => Real.log (f x)

full_name: Measurable.cos
code: @[measurability]
theorem Measurable.cos : Measurable fun x => Real.cos (f x) 
goal: Measurable fun x => Real.cos (f x)

full_name: Measurable.sin
code: @[measurability]
theorem Measurable.sin : Measurable fun x => Real.sin (f x) 
goal: Measurable fun x => Real.sin (f x)

full_name: Measurable.cosh
code: @[measurability]
theorem Measurable.cosh : Measurable fun x => Real.cosh (f x) 
goal: Measurable fun x => Real.cosh (f x)

full_name: Measurable.sinh
code: @[measurability]
theorem Measurable.sinh : Measurable fun x => Real.sinh (f x) 
goal: Measurable fun x => Real.sinh (f x)

full_name: Measurable.sqrt
code: @[measurability]
theorem Measurable.sqrt : Measurable fun x => √(f x) 
goal: Measurable fun x => √(f x)

full_name: Measurable.cexp
code: @[measurability]
theorem Measurable.cexp : Measurable fun x => Complex.exp (f x) 
goal: Measurable fun x => Complex.exp (f x)

full_name: Measurable.ccos
code: @[measurability]
theorem Measurable.ccos : Measurable fun x => Complex.cos (f x) 
goal: Measurable fun x => Complex.cos (f x)

full_name: Measurable.csin
code: @[measurability]
theorem Measurable.csin : Measurable fun x => Complex.sin (f x) 
goal: Measurable fun x => Complex.sin (f x)

full_name: Measurable.ccosh
code: @[measurability]
theorem Measurable.ccosh : Measurable fun x => Complex.cosh (f x) 
goal: Measurable fun x => Complex.cosh (f x)

full_name: Measurable.csinh
code: @[measurability]
theorem Measurable.csinh : Measurable fun x => Complex.sinh (f x) 
goal: Measurable fun x => Complex.sinh (f x)

full_name: Measurable.carg
code: @[measurability]
theorem Measurable.carg : Measurable fun x => arg (f x) 
goal: Measurable fun x => (f x).arg

full_name: Measurable.clog
code: @[measurability]
theorem Measurable.clog : Measurable fun x => Complex.log (f x) 
goal: Measurable fun x => Complex.log (f x)

full_name: Complex.hasMeasurablePow
code: instance Complex.hasMeasurablePow : MeasurablePow ℂ ℂ 
goal: MeasurablePow ℂ ℂ

full_name: Real.hasMeasurablePow
code: instance Real.hasMeasurablePow : MeasurablePow ℝ ℝ 
goal: MeasurablePow ℝ ℝ

full_name: NNReal.hasMeasurablePow
code: instance NNReal.hasMeasurablePow : MeasurablePow ℝ≥0 ℝ 
goal: MeasurablePow ℝ≥0 ℝ

full_name: ENNReal.hasMeasurablePow
code: instance ENNReal.hasMeasurablePow : MeasurablePow ℝ≥0∞ ℝ 
goal: MeasurablePow ℝ≥0∞ ℝ