Let (left(u_{n}, mathscr{A}_{n}ight)_{n in mathbb{N}}) be a supermartingale and (u_{n} geqslant 0) a.e. Prove that (u_{k}=0) a.e.

Question:

Let \(\left(u_{n}, \mathscr{A}_{n}ight)_{n \in \mathbb{N}}\) be a supermartingale and \(u_{n} \geqslant 0\) a.e. Prove that \(u_{k}=0\) a.e. implies that \(u_{k+n}=0\) a.e. for all \(n \in \mathbb{N}\).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: