AWhat changed
A mean/postulate-sensitive order family extends the Shannon limiting case and characterizes finite generalized information measures without equating weaker additivity to full grouping.
Scientific scope
A mean/postulate-sensitive order family extends the Shannon limiting case and characterizes finite generalized information measures without equating weaker additivity to full grouping. Finite discrete distributions, plus generalized nonnegative weights with 0<W<=1. Independent-product additivity is weaker than Shannon grouping: the order-parametrized entropy family does not inherit every Shannon chain rule. Shannon arises as order tends to 1; exponential versus arithmetic means and stated postulates distinguish the family. Information characterization uses matched finite supports with positive reference probabilities; section 3 explicitly needs an extra continuity postulate to exclude nonpositive orders. The opening Radon–Nikodym discussion is not a proof of every infinite/continuous extension. The Markov illustration assumes finitely many states, strictly positive one-step transitions and an inherited positive stationary distribution; it supplies convergence, not a finite burn-in bound or every irreducible chain theorem. Existing KL and Markov limit results are not claimed as first here. no independent proof, estimator performance, quantum-entropy result or universal measure of scientific value. Earlier 1959/1960 work and 1961 selected edition are distinguished without duplicate entries.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Alfréd Rényi · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Rényi, On Measures of Entropy and Information (1961), original 547–561
- Rényi Institute author bibliography:1961 entropy chapter entry
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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