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Theorems · Theorem · measure theory

ENNReal.tsum_iUnion_le_tsum

∀ {α : Type u_1} {ι : Type u_4} (f : α → ENNReal) (t : ι → Set α),
  ∑' (x : ↑(⋃ i, t i)), f ↑x ≤ ∑' (i : ι) (x : ↑(t i)), f ↑x
Defined in
Mathlib.Topology.Algebra.InfiniteSum.ENNReal
Cited by
2 results in Mathlib
Foundations
Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

ENNReal.tsum_iUnion_le · cited by 2ENNReal.tsum_iUnion_leENNReal.tsum_biUnion_le_tsum · cited by 1ENNReal.tsum_biUnion_le_t…Set · cited by 53352SetENNReal · cited by 9879ENNRealSet.Elem · cited by 7166Set.ElemSet.iUnion · cited by 2483Set.iUnionSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…tsum · cited by 1148tsumSet.sigmaToiUnion_surjective · cited by 4Set.sigmaToiUnion_surject…ENNReal.tsum_sigma' · cited by 2ENNReal.tsum_sigma'ENNReal.tsum_le_tsum_comp_of_surjective · cited by 1ENNReal.tsum_le_tsum_comp…ENNReal.tsum_iUnion_le_tsumCITED BYCITES

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Cited by2

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