Theorems · Theorem · number theory
Nat.Primes.tsum_eq_tsum_ite
∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M] (f : ℕ → M),
∑' (p : Nat.Primes), f ↑p = ∑' (n : ℕ), if Nat.Prime n then f n else 0Reindex a sum over Nat.Primes as a sum over ℕ, extending f by 0.
- Defined in
- Mathlib.NumberTheory.SumPrimeReciprocals
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Set.ofPredproof · cited by 6,101
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
- tsumstatement and proof · cited by 1,148
- Nat.Primesstatement and proof · cited by 63
- tsum_subtypeproof · cited by 6
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