In a paper I'm reading, it refers to Theorem 8, Page 217 of the book

"Introduction to Stochastic Control" H. J. Kushner, New York: Holt, Reinhart, and Winston 1971. Unfortunately I don't have it and the copy in our library was checked out.

Does anyone here happen to have that book at hand and let me know what the theorem says?

It's a stochastic version of LaSalle's Theorem.

Thanks!!