A note on the irreducibility of Lebesgue measure with applications to random walks on the unit circle
Author: Tzuu Shuh Chiang
Journal: Proc. Amer. Math. Soc. 85 (1982), 603-605
MSC: Primary 60J15; Secondary 28A12, 46G99
MathSciNet review: 660613
Abstract: Let be a probability measure on . We say that a -finite measure is irreducible with respect to if there does not exist a Borel set with , such that . It is well known that the Lebesgue measure is irreducible with respect to any discrete measure whose support is . We prove that every absolutely continuous measure is irreducible with respect to any probability measure whose support is and give an application of this fact to random walks on the unit circle.