Mathlib Map

Theorems · Definition · complex analysis

Function.locallyFinsuppWithin.toClosedBall

{E : Type u_1} →
  [inst : NormedAddCommGroup E] →
    (r : ℝ) → Function.locallyFinsupp E ℤ →+ Function.locallyFinsuppWithin (Metric.closedBall 0 |r|) ℤ

Shorthand notation for the restriction of a function with locally finite support to the closed unit ball of radius r.

Defined in
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic
Cited by
10 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroup

Around this declaration

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

Function.locallyFinsuppWithin.logCounting · cited by 36locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_const · cited by 4locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.toClosedBall_eval_within · cited by 3locallyFinsuppWithin.toCl…Function.locallyFinsuppWithin.logCounting_nonneg · cited by 3locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_eval_zero · cited by 2locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_mono · cited by 2locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.toClosedBall_divisor · cited by 1locallyFinsuppWithin.toCl…Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall · cited by 1locallyFinsuppWithin.toCl…ValueDistribution.characteristic_sub_characteristic_inv_of_ne_zero · cited by 1ValueDistribution.charact…Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const · cited by 1locallyFinsuppWithin.logC…Function.locallyFinsuppWithin.logCounting_even · cited by 1locallyFinsuppWithin.logC…Real · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupSet.univ · cited by 3945Set.univAddMonoidHom · cited by 3230AddMonoidHomabs · cited by 1814absMetric.closedBall · cited by 704Metric.closedBallFunction.locallyFinsuppWithin · cited by 127Function.locallyFinsuppWi…Function.locallyFinsupp · cited by 43Function.locallyFinsuppFunction.locallyFinsuppWithin.restrictMonoidHom · cited by 2locallyFinsuppWithin.rest…locallyFinsuppWithin.toClosed…CITED BYCITES

Cites9

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Cited by11

Results whose statement or proof uses this declaration.