Theorems · Theorem · complex analysis

Function.locallyFinsuppWithin.logCounting_strictMono

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : DecidableEq E] [inst_2 : ProperSpace E]
  {D : Function.locallyFinsupp E ℤ} {e : E},
  Function.locallyFinsuppWithin.single e 1 ≤ D →
    StrictMonoOn (Function.locallyFinsuppWithin.logCounting D) (Set.Ioi ‖e‖)

The logarithmic counting function of a positive function with locally finite support is asymptotically strictly monotone.

Defined in: Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup DecidableEq ProperSpace

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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map_subproof · cited by 565

Cited by1

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Function.locallyFinsuppWithin.zero_iff_logCounting_boundedproof · cited by 1