Operations On Partitions
Given a partition Q = {Q1, ..., Qk} and a dynamical system, we define T-pullback of Q as
Further, given two partitions Q = {Q1, ..., Qk} and R = {R1, ..., Rm}, we define their refinement as
With these two constructs we may define refinement of an iterated pullback
which plays crucial role in the construction of the measure-theoretic entropy of a dynamical system.
Read more about this topic: Measure-preserving Dynamical System
Famous quotes containing the words operations and/or partitions:
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—Jean Scott Rogers. Robert Day. Mr. Blount (Frank Pettingell)
“Great wits are sure to madness near allied,
And thin partitions do their bounds divide.”
—John Dryden (1631–1700)