Invariant Probabilities of Transition Functions by Radu Zaharopol

Author:Radu Zaharopol
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Assertion A.

and for every x ∈ (0, 1).

In order to prove the assertion, we have to show that exists and is equal to f(0) for every continuous function and every x ∈ (0, 1).

To this end, let be a continuous function and let x ∈ (0, 1).

Clearly, the assertion is true if f = 0, so we may and do assume that f ≠ 0. Thus, .

Now, let , .

Since f is a continuous function and since , it follows that there exists a , , large enough such that for every , .

Now, there exists a , , large enough such that .

We obtain that

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.