Theorems · Theorem · measure theory
ENNReal.tsum_mul_left
∀ {α : Type u_1} {a : ENNReal} {f : α → ENNReal}, ∑' (i : α), a * f i = a * ∑' (i : α), f i- Cited by
- 21 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- nhdsproof · cited by 5,554
- Finset.sumproof · cited by 5,195
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Summable.hasSumproof · cited by 184
- HasSum.tsum_eqproof · cited by 150
- tsum_zeroproof · cited by 63
Cited by21
Results whose statement or proof uses this declaration.
- ENNReal.tsum_mul_rightproof · cited by 5
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- PMF.bind_bindproof · cited by 3
- edist_le_of_edist_le_geometric_of_tendstoproof · cited by 3
- cauchySeq_of_edist_le_geometricproof · cited by 2
- PMF.toOuterMeasure_bind_applyproof · cited by 2
- MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1proof · cited by 1
- ProbabilityTheory.Kernel.IndepSets.indep_auxproof · cited by 1
- ENNReal.tsum_geometric_add_oneproof · cited by 1
- Vitali.exists_disjoint_covering_aeproof · cited by 1
- MeasureTheory.Egorov.measure_iUnionNotConvergentSeqproof · cited by 1
- MeasureTheory.Measure.exists_null_set_measure_lt_of_disjointproof · cited by 1