Theorems · Definition · real analysis
ENNReal.orderIsoRpow
(y : ℝ) → 0 < y → ENNReal ≃o ENNReal
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
- 3 results in Mathlib
- Foundations
- Depth 204 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
- ENNRealstatement and proof · cited by 9,879
- OrderIsostatement · cited by 874
- ENNReal.strictMono_rpow_of_posproof · cited by 7
- StrictMono.orderIsoOfRightInverseproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_bdd_liminf_atTop_of_eLpNorm_bddproof · cited by 1
- ENNReal.orderIsoRpow_applystatement and proof · cited by 0
- ENNReal.orderIsoRpow_symm_applystatement · cited by 0