不變測可以由它們的投影來研究。特別是關於不變測度的質心的研究近幾年受到不少關注。陳國璋和董遜(2010[3]) 發現一套方法使得不同的Tent映射的軌道有相同的質心。這可以看做是許多不同的不變測度有重疊的投影在f(x)=x這方向上。這驅使我們考慮:什麼情況下，不同的兩個轉化下所對應的不變測度能擁有重疊的投影在某個方向上?這篇論文目的即是討論此問題。

Invariant probability measures can be studied through their projections.
In particular, the study of barycenters of these invariant measures has received
much attention in resent years. K.C.Chen and X.Dong (2010 [3]) found a
way to construct different orbits with the same barycenter for the tent map. It can
be seen as that many invariant measures have overlapped projection along the
direction f(x) = x. This motivates us to consider: when can invariant measures
corresponding to two distinct transformations have overlapped projection
along some direction? This thesis aims to discuss this problem.

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