Commit 2023-01-31 19:36 59694bd0
View on Github →feat(measure_theory/integral/peak_function): convergence of integral against a sequence of peak functions (#18327)
If a sequence of peak functions φᵢ
converges uniformly to zero away from a point x₀
, and g
is integrable and continuous at x₀
, then ∫ φᵢ • g
converges to g x₀
. We prove this statement and some consequences of it (notably to sequences which are the successive powers of a given function).