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Theorems · Theorem · general topology

NNReal.summable_coe

∀ {α : Type u_2} {L : SummationFilter α} {f : α → NNReal}, Summable (fun a => ↑(f a)) L ↔ Summable f L
Defined in
Mathlib.Topology.Instances.NNReal.Lemmas
Cited by
15 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.

Summable.of_nonneg_of_le · cited by 36Summable.of_nonneg_of_leSummable.of_nnnorm_bounded · cited by 4Summable.of_nnnorm_boundedNNReal.summable_comp_injective · cited by 3NNReal.summable_comp_inje…MeasureTheory.setToFun_tsum · cited by 3MeasureTheory.setToFun_ts…ENNReal.tsum_coe_ne_top_iff_summable_coe · cited by 2ENNReal.tsum_coe_ne_top_i…NNReal.summable_nat_add_iff · cited by 2NNReal.summable_nat_add_i…MeasureTheory.hasSum_integral_of_summable_integral_norm · cited by 2MeasureTheory.hasSum_inte…HasFPowerSeriesWithinAt.comp · cited by 2HasFPowerSeriesWithinAt.c…Summable.toNNReal · cited by 1Summable.toNNRealSummable.countable_support_nnreal · cited by 1Summable.countable_suppor…MeasureTheory.integrableOn_iUnion_of_summable_integral_norm · cited by 1MeasureTheory.integrableO…FormalMultilinearSeries.summable_nnnorm_mul_pow · cited by 1FormalMultilinearSeries.s…HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp · cited by 1HasFPowerSeriesAt.tendsto…NNReal.summable_mk · cited by 0NNReal.summable_mktsum_comp_le_tsum_of_inj · cited by 0tsum_comp_le_tsum_of_injReal · cited by 25697RealFinset · cited by 13712Finsetnhds · cited by 5554nhdsFinset.sum · cited by 5195Finset.sumBot.bot · cited by 4720Bot.botNNReal · cited by 4310NNRealFilter.Tendsto · cited by 3814Filter.TendstoFinset.sum_congr · cited by 2323Finset.sum_congrNNReal.toReal · cited by 1260NNReal.toRealSummable · cited by 778SummableSummationFilter · cited by 607SummationFilterHasSum · cited by 518HasSumSummationFilter.NeBot · cited by 130SummationFilter.NeBotSummationFilter.filter · cited by 110SummationFilter.filterNNReal.hasSum_coe · cited by 8NNReal.hasSum_coeNNReal.summable_coeCITED BYCITES

Cites17

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Cited by15

Results whose statement or proof uses this declaration.