tendsto_rpow_atBot_of_base_gt_one

English

The set Set.univ.pi polarCoord.target is measurable.

Русский

Множество Set.univ.pi polarCoord.target измеримо.

LaTeX

$$$\text{MeasurableSet}(\text{Set.univ.pi}(\text{polarCoord.target})).$$$

Lean4

theorem tendsto_rpow_atBot_of_base_gt_one (b : ℝ) (hb : 1 < b) : Tendsto (b ^ · : ℝ → ℝ) atBot (𝓝 0) :=
  by
  simp_rw [Real.rpow_def_of_pos (by positivity : 0 < b)]
  refine tendsto_exp_atBot.comp <| (tendsto_const_mul_atBot_of_pos ?_).mpr tendsto_id
  exact (log_pos_iff (by positivity)).mpr <| by aesop

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