Theorems · Theorem · real analysis
ENNReal.mul_iSup
∀ {ι : Sort u_1} (a : ENNReal) (f : ι → ENNReal), a * ⨆ i, f i = ⨆ i, a * f i- Defined in
- Mathlib.Data.ENNReal.Inv
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.topproof · cited by 9,680
- iSupstatement and proof · cited by 2,415
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- Iff.notproof · cited by 489
- Eq.geproof · cited by 375
- Topproof · cited by 93
- le_iSup_of_leproof · cited by 79
- ENNReal.top_mulproof · cited by 29
- OrderIso.map_iSupproof · cited by 25
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasureTheory.lintegral_iSupproof · cited by 16
- MeasureTheory.lintegral_withDensity_eq_lintegral_mulproof · cited by 5
- ENNReal.iSup_mulproof · cited by 5
- HolderOnWith.hausdorffMeasure_image_leproof · cited by 2
- ENNReal.smul_iSupproof · cited by 2
- MeasureTheory.lintegral_const_mul_leproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.smulproof · cited by 2
- AntilipschitzWith.hausdorffMeasure_preimage_leproof · cited by 2
- MeasureTheory.SimpleFunc.lintegral_restrict_iUnion_of_directedproof · cited by 1