Theorems · Theorem · real analysis
ENNReal.rpow_lt_top_of_nonneg
∀ {x : ENNReal} {y : ℝ}, 0 ≤ y → x ≠ ⊤ → x ^ y < ⊤- Cited by
- 14 results in Mathlib
- Foundations
- Depth 205 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
- Top.topstatement and proof · cited by 9,680
- lt_top_iff_ne_topproof · cited by 95
- ENNReal.rpow_ne_top_of_nonnegproof · cited by 7
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_topproof · cited by 9
- MeasureTheory.lpNorm_eq_integral_norm_rpow_toRealproof · cited by 3
- MeasureTheory.MemLp.norm_rpow_divproof · cited by 2
- MeasureTheory.MemLp.enorm_rpow_divproof · cited by 2
- ENNReal.LpAddConst_lt_topproof · cited by 2
- ProbabilityTheory.evariance_eq_topproof · cited by 2
- MeasureTheory.lintegral_rpow_enorm_lt_top_of_eLpNorm'_lt_topproof · cited by 2
- eHolderNorm_eq_zeroproof · cited by 1
- MeasureTheory.ae_bdd_liminf_atTop_of_eLpNorm_bddproof · cited by 1
- MeasureTheory.eLpNorm'_lt_top_of_eLpNorm'_lt_top_of_exponent_leproof · cited by 1
- MeasureTheory.SimpleFunc.memLp_of_finite_measure_preimageproof · cited by 1