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首页> 外文期刊>Real analysis exchange >THE DYNAMICS OF A TYPICAL MEASURABLE FUNCTION ARE DETERMINED ON A ZERO MEASURE SET
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THE DYNAMICS OF A TYPICAL MEASURABLE FUNCTION ARE DETERMINED ON A ZERO MEASURE SET

机译：在零测量集上确定典型可测量功能的动态

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Let A be a zero measure dense Gg subset of I = [0,1], with M the set of measurable self-maps of I. There exists a residual set R < M. such that for each f in R, the range of f is contained in A, and the function f is one-to-one. Moreover, there exists h : I → I a Baire-2 function such that f(x) = h(x) a.e., and for any x ∈ I, the trajectory T(x,h) is ∞-adic, so that the ω-limit set ω(x, h) is a Cantor set. Since the range of / is contained in A, it follows that for any x in I, there exists y in A such that the trajectory T(f(x),F) = T(y, f)< A. Speaking loosely, the dynamical structures of f are completely determined by its behavior on the set A.
机译：让A为零测量致密的GG子集i = [0,1]，用M的一组可测量的自我图。存在残留的设置R

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