【摘要】：設(shè)β1為實(shí)數(shù),T_β為[0,1]的β變換.攀援集的任何兩個(gè)點(diǎn)隨著時(shí)間的轉(zhuǎn)移會(huì)越來(lái)越接近但同時(shí)又總能在任意長(zhǎng)時(shí)間后保持一定的距離.證明了在Lebesgue測(cè)度意義下關(guān)于T_β的攀援集是一個(gè)零測(cè)集.Distal點(diǎn)對(duì)的兩個(gè)點(diǎn)表示隨著時(shí)間的轉(zhuǎn)移始終保持著一定的距離.如果固定其中一個(gè)點(diǎn)x_0,所有滿足x∈[0,1)且lim inf n→∞|T_β~n(x)-T_β~n(x_0)|0的點(diǎn)稱為關(guān)于x_0的distal集,如果把這個(gè)集合記為R_β(x_0),根據(jù)Borel-Cantelli引理得到R_β(x_0)的Lebesgue測(cè)度為零.
[Abstract]:Let 尾 _ 1 be a real number and T _ 尾 be a 尾 -transformation of [0]. Any two points in the climbing set will get closer and closer over time, but at the same time they can keep a certain distance after any long time. It is proved that the climbing set of T _ 尾 in the sense of Lebesgue measure is a zero measure set, and that the two points of Distal point pair always keep a certain distance with the time transfer. If one of the points x0 is fixed, all the points satisfying x 鈭，

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