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Theorems · Theorem · measure theory

ENNReal.tsum_le_tsum

∀ {α : Type u_1} {f g : α → ENNReal}, (∀ (a : α), f a ≤ g a) → ∑' (a : α), f a ≤ ∑' (a : α), g a
Defined in
Mathlib.Topology.Algebra.InfiniteSum.ENNReal
Cited by
43 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae · cited by 5TendstoInMeasure.exists_s…VitaliFamily.measure_le_of_frequently_le · cited by 5VitaliFamily.measure_le_o…MeasureTheory.OuterMeasure.le_ofFunction · cited by 5OuterMeasure.le_ofFunctionMeasureTheory.addHaar_image_le_mul_of_det_lt · cited by 4MeasureTheory.addHaar_ima…MeasureTheory.OuterMeasure.comap_iInf · cited by 3OuterMeasure.comap_iInfPMF.tsum_coe_indicator_ne_top · cited by 3PMF.tsum_coe_indicator_ne…volume_iUnion_setOfPred_liouvilleWith · cited by 2volume_iUnion_setOfPred_l…MeasureTheory.OuterMeasure.ofFunction_caratheodory · cited by 2OuterMeasure.ofFunction_c…MeasureTheory.OuterMeasure.ofFunction_union_of_top_of_nonempty_inter · cited by 2OuterMeasure.ofFunction_u…MeasureTheory.OuterMeasure.comap_ofFunction · cited by 2OuterMeasure.comap_ofFunc…HolderOnWith.hausdorffMeasure_image_le · cited by 2HolderOnWith.hausdorffMea…MeasureTheory.exists_le_lowerSemicontinuous_lintegral_ge · cited by 2MeasureTheory.exists_le_l…StieltjesFunction.outer_Ioc · cited by 2StieltjesFunction.outer_I…AntilipschitzWith.hausdorffMeasure_preimage_le · cited by 2AntilipschitzWith.hausdor…MeasureTheory.Measure.sum_apply₀ · cited by 2Measure.sum_apply₀ENNReal · cited by 9879ENNRealSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…tsum · cited by 1148tsumENNReal.summable · cited by 59ENNReal.summableSummable.tsum_le_tsum · cited by 27Summable.tsum_le_tsumENNReal.tsum_le_tsumCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by43

Results whose statement or proof uses this declaration.