Theorems · Theorem · real analysis
tendsto_rpow_atTop
∀ {y : ℝ}, 0 < y → Filter.Tendsto (fun x => x ^ y) Filter.atTop Filter.atTopThe function x ^ y tends to +∞ at +∞ for any positive real y.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- one_divproof · cited by 624
- Filter.eventually_ge_atTopproof · cited by 111
- Filter.HasBasis.tendsto_right_iffproof · cited by 81
- Filter.atTop_basis'proof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- isLittleO_log_rpow_atTopproof · cited by 3
- LiouvilleWith.frequently_lt_rpow_negproof · cited by 3
- tendsto_exp_mul_div_rpow_atTopproof · cited by 3
- tendsto_rpow_neg_atTopproof · cited by 3
- ZLattice.covolume.tendsto_card_le_div''proof · cited by 2
- ZetaAsymptotics.termTSum_of_ltproof · cited by 2
- exp_neg_mul_rpow_isLittleO_exp_negproof · cited by 2
- tendsto_rpow_neg_nhdsGT_zeroproof · cited by 1
- isLittleO_log_rpow_rpow_atTopproof · cited by 1
- Real.tendsto_integral_gaussian_smul'proof · cited by 1
- NNReal.tendsto_rpow_atTopproof · cited by 1
- MeasureTheory.integral_comp_rpow_Ioi_of_pos'proof · cited by 0