Theorems · Theorem · real analysis
ContinuousOn.log
∀ {α : Type u_1} [inst : TopologicalSpace α] {f : α → ℝ} {s : Set α},
ContinuousOn f s → (∀ x ∈ s, f x ≠ 0) → ContinuousOn (fun x => Real.log (f x)) s- Cited by
- 11 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- Real.logstatement · cited by 939
- ContinuousWithinAt.logproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- MeromorphicOn.intervalIntegrable_log_normproof · cited by 4
- Real.tendstoLocallyUniformlyOn_rpow_sub_one_logproof · cited by 2
- IntervalIntegrable.logproof · cited by 1
- integral_inv_div_logproof · cited by 0
- integral_inv_div_log_sqproof · cited by 0
- CFC.continuousOn_logproof · cited by 0
- CFC.log_expproof · cited by 0
- CFC.log_powproof · cited by 0
- CFC.log_smulproof · cited by 0
- CFC.exp_logproof · cited by 0