Theorems · Theorem · measure theory
NNReal.summable_of_le
∀ {β : Type u_2} {f g : β → NNReal}, (∀ (b : β), g b ≤ f b) → Summable f → Summable gComparison test of convergence of ℝ≥0-valued series.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Summablestatement and proof · cited by 778
- HasSumproof · cited by 518
- HasSum.summableproof · cited by 98
- NNReal.exists_le_hasSum_of_leproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- Summable.of_nonneg_of_leproof · cited by 36
- Memℓp.const_smulproof · cited by 3
- FormalMultilinearSeries.changeOrigin_radiusproof · cited by 3
- NNReal.tsum_lt_tsumproof · cited by 2
- FormalMultilinearSeries.comp_summable_nnrealproof · cited by 2
- NNReal.indicator_summableproof · cited by 1
- FormalMultilinearSeries.changeOriginSeries_summable_aux₃proof · cited by 1
- NNReal.tsum_eq_add_tsum_iteproof · cited by 0