def definition def or abbrev

`shannonEntropy`

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

formal statement (Lean)

  67noncomputable def shannonEntropy {n : ℕ} (d : ProbDist n) : ℝ :=

proof body

Definition body.

  68  -(Finset.univ.sum fun i =>
  69    if d.probs i > 0 then d.probs i * Real.log (d.probs i)
  70    else 0)
  71
  72/-- **THEOREM**: Entropy is non-negative. -/

used by (9)

From the project-wide theorem graph. These declarations reference this one in their body.

deterministic_has_zero_entropy in IndisputableMonolith.Information.InformationIsLedger decl_use
entropy_nonneg in IndisputableMonolith.Information.InformationIsLedger decl_use
shannon_entropy_equals_expected_jcost in IndisputableMonolith.Information.InformationIsLedger decl_use
uniform_has_max_entropy in IndisputableMonolith.Information.InformationIsLedger decl_use
entropy_is_expected_surprisal in IndisputableMonolith.Information.ShannonEntropy decl_use
entropy_nonneg in IndisputableMonolith.Information.ShannonEntropy decl_use
max_entropy_uniform in IndisputableMonolith.Information.ShannonEntropy decl_use
shannon_equals_jcost in IndisputableMonolith.Information.ShannonEntropy decl_use
zero_entropy_deterministic in IndisputableMonolith.Information.ShannonEntropy decl_use

depends on (6)

Lean names referenced from this declaration's body.

is in IndisputableMonolith.Foundation.OptionAEmpiricalProgram decl_use
is in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi decl_use
is in IndisputableMonolith.GameTheory.MechanismDesignFromSigma decl_use
ProbDist in IndisputableMonolith.Information.ShannonEntropy decl_use
is in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom decl_use
ProbDist in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use