Theorems · Theorem · real analysis
ENNReal.mul_lt_top_iff
∀ {a b : ENNReal}, a * b < ⊤ ↔ a < ⊤ ∧ b < ⊤ ∨ a = 0 ∨ b = 0- Defined in
- Mathlib.Data.ENNReal.Operations
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.neproof · cited by 872
- ENNReal.mul_lt_topproof · cited by 41
- ENNReal.lt_top_of_mul_ne_top_rightproof · cited by 2
- ENNReal.lt_top_of_mul_ne_top_leftproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_const_lt_top_iff_enormproof · cited by 2
- MeasureTheory.eLpNorm'_lt_top_of_eLpNorm'_lt_top_of_exponent_leproof · cited by 1
- MeasureTheory.integrable_smul_constproof · cited by 1
- ENNReal.mul_self_lt_top_iffproof · cited by 0