本文主要是探討在二維投影空間上的不變測度的唯一性.在Gu中任一矩陣之行列式的絕對值均為1以及Gu為非緊緻集的條件下,我們有以下的結果:
(1)如果在二維投影空間上任意的元素x,
{M．x|M 屬於 Gu}這個集合的元素個數大於或等於3,
則此時不變測度是唯一的.
(2)如果在二維投影空間上有一個元素x,存在相異兩點
x1,x2使得{M．x|M 屬於Gu}包含於{x1,x2},若x1和
x2都被固定住,則此時不變測度並非唯一;否則,
僅在x1和x2上有測度值的不變測度是唯一的.

In 2 ×2 case,we discuss the uniqueness of the
u-invariant measure on projective space.Under the condition that |detM|=1 for any M in Gu and Gu is not compact,we have the followings:
(1) For any x in P(R^2),if #{M．x|M belongs Gu}>2, then the u-invariant measure is unique.
(2) For some x in P(R^2),there exists
x1,x2 such that {M．x|M belongs Gu} is contained in {x1,x2},if x1 and x2 are both fixed,then the
u-invariant measure v is not unique;otherwise,if u has mass only on x1 and x2,then the u-invariant
measure is unique.

Introduction．．．．．．．．．．．．．．．．．．1
Invariant Measure In 2 ×2 case ．．．．．．．．4
References ．．．．．．．．．．．．．．．．．．10

1.H. Furstenberg and H. Kesten (1960),
Products of Random Matrices,
Ann. Math. Stat,31, 457-469.
2.H. Furstenberg and Y. Kifer (1983),
Random Matrix Products And Measures On Projective Spaces,
Israel Journal Of Mathematics,Vol. 46, 19-20.
3.P. Bougerol and J. Lacroix(1985),
Products of Random Matrices with Applications to Schrodinger Operators,
Birkhauser.