Theorems · Definition · real analysis
NNReal.rpow
NNReal → ℝ → NNReal
The nonnegative real power function x^y, defined for x : ℝ≥0 and y : ℝ as the
restriction of the real power function. For x > 0, it is equal to exp (y log x). For x = 0,
one sets 0 ^ 0 = 1 and 0 ^ y = 0 for y ≠ 0.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- NNReal.toRealproof · cited by 1,260
Cited by5
Results whose statement or proof uses this declaration.
- ENNReal.rpow_zeroproof · cited by 47
- ENNReal.zero_rpow_of_posproof · cited by 36
- ENNReal.coe_rpow_of_ne_zeroproof · cited by 20
- ENNReal.zero_rpow_of_negproof · cited by 12
- NNReal.rpow_eq_powstatement · cited by 0