Theorems · Theorem · real analysis
tendsto_rpow_neg_atTop
∀ {y : ℝ}, 0 < y → Filter.Tendsto (fun x => x ^ (-y)) Filter.atTop (nhds 0)The function x ^ (-y) tends to 0 at +∞ for any positive real y.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Set.Ioiproof · cited by 1,463
- le_of_ltproof · cited by 1,175
- Filter.Tendsto.congr'proof · cited by 154
- Real.rpow_negproof · cited by 36
- Filter.Ioi_mem_atTopproof · cited by 36
- Filter.eventuallyEq_of_memproof · cited by 25
- Filter.Tendsto.inv_tendsto_atTopproof · cited by 21
- tendsto_rpow_atTopproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- integral_Ioi_rpow_of_ltproof · cited by 2
- integrableOn_add_rpow_Ioi_of_ltproof · cited by 1
- integral_Ioi_cpow_of_ltproof · cited by 0