Manuscript Psy03-C@1 · Psy03-C-v1.tex · proposition · d3380b90

Proposition: Information invariance under invertible transformations

Probe geometry and exact task references › Invertible shift versus unavailable task identity · lines 1151–1164 · proof included or linked

Psy03-C@1#prop:invertible

For a measurable invertible transformation $T$ , with measurable inverse and unchanged label,

Q^{*} (T (X)) = Q^{*} (X) .

Consequently positive scaling and fixed rotation preserve ideal label information.

Proof. Compose prediction rules with $T$ or $T^{- 1}$ .

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