Kolmogorov extension theorem on a smaller sigma-algebra

74 Views Asked by At

I am taking a Probability class and I am struggling with an exercise on Kolmogorov extension theorem.

It asks to prove that there exists a probabiity measure on the cyinder $\sigma$-algebra of $\lbrace 0,1 \rbrace^\infty$.

I think that it would be enough to start from $\lbrace 0,1 \rbrace^N$ defining a probability measure on $\sigma$-algebra of $\lbrace 0,1 \rbrace^N$ and proving that it satisfies the two consistency conditions, am I right?

Thank you in advance