Theorems · Definition · real analysis
NNReal.orderIsoRpow
(y : ℝ) → 0 < y → NNReal ≃o NNReal
Bundles fun x : ℝ≥0 => x ^ y into an order isomorphism when y : ℝ is positive,
where the inverse is fun x : ℝ≥0 => x ^ (1 / y).
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- NNRealstatement and proof · cited by 4,310
- OrderIsostatement · cited by 874
- StrictMono.orderIsoOfRightInverseproof · cited by 5
- NNReal.strictMono_rpow_of_posproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- NNReal.strictConcaveOn_rpowproof · cited by 3
- NNReal.orderIsoRpow_applystatement and proof · cited by 1
- NNReal.orderIsoRpow_symm_eqstatement · cited by 1
- NNReal.orderIsoRpow.congr_simpstatement and proof · cited by 1