add poisson distribution#1668
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affeldt-aist merged 2 commits intoJul 3, 2025
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Very welcomed addition!
esum_limn_ge0 can actually be proved as follows:
Local Open Scope classical_set_scope.
Local Open Scope ring_scope.
Variables (R : realType).
Context {f : nat -> R}.
Hypothesis (f0 : forall n, 0 <= f n).
Lemma esum_limn_ge0 :
\esum_(i in [set: nat]) (f i)%:E
= limn
(EFin \o (fun n : nat => (\sum_(0 <= k < n) f k)%R)).
Proof.
rewrite -set_true -nneseries_esum//; last by move=> *; rewrite lee_fin.
by apply/congr_lim/funext => n/=; rewrite -sumEFin.
Qed.
End elim_limn_ge0.which suggests that the lemma is moderately useful.
In fact, it is a bit shorter to prove poisson_setT
by moving from esum to nneseries where there are
more lemmas (and this proof does not require esum_limn_ge0).
I have therefore removed it.
On the other hand, this also suggests that nneseries_esum
is a bit awkward to use when use with the whole set, I have
therefore added the technical lemma nneseries_esumT
and this helps a bit imo.
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Motivation for this change
Adding Poisson distribution.
Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
Merge policy
As a rule of thumb:
all compile are preferentially merged into master.
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