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Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.
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참고문헌 (8)
참고문헌 신청
A. Boyarsky / 1997 / Laws of Chaos / Birkh¨auser
G. H. Choe / 2004 / Skew product and mod 2 normal numbers / Studia Math 165:53~60
E. Hewitt / 1963 / Abstract Harmonic Analysis I, II / Springer-Verlag
E. Hlawka / 1984 / The Theory of Uniform Distribution / A B Academic publishers
W. Parry / 1992 / A Cocycle equation for shift / Contemp. Math 135:327~333
G. H. Choe / 2004 / Skew product and mod 2 normal numbers / Studia Math 165:53~60
E. Hewitt / 1963 / Abstract Harmonic Analysis I, II / Springer-Verlag
E. Hlawka / 1984 / The Theory of Uniform Distribution / A B Academic publishers
W. Parry / 1992 / A Cocycle equation for shift / Contemp. Math 135:327~333
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