Flows and Their Representations

Part of the Texts and Readings in Mathematics book series (volume 6)


Let (X, Ɓ) be a standard Borel space. A group τ t , t ∈ ℝ, of Borel automorphisms on (X, Ɓ) is called a jointly measurable flow, or simply a flow, if
  1. (i)

    the map (t, x) ↦ τ t x from ℝ × XX is measurable, where ℝ × X is given the usual product Borel structure,

  2. (ii)

    τ0x = x for all xX,

  3. (iii)

    τ0x = τt ο τ s (x) for all t,s ∈ ℝ and all x ∈ ℝ.



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© Hindustan Book Agency 2013

Authors and Affiliations

  1. 1.University of MumbaiIndia

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