Ergodic theory: Let X=[0,1]; m is lebesgue measure,

[mikecaster]

Let X=[0,1] ; m is lebesgue measure , s is sigma algebra and (X,s,m) is a probability space. We define operator

T:[0,1] --> [0,1]
T(x)= 2x(mod 1) i.e. 2x for 0<= x <1/2 and 2x-1 for 1/2<= x <=1

what can we say about the followings, how can we show these are true or false..

a)T preserves measure

b)There is a point x with periodic trajectory

c)for any given natural N, there is a point x with period N

d)the set of all periodic points is dense in X

e)there is a point with dense trajectory

f)transformation T is ergodic

thanks..