1. ## Borel Fields

Hi, I was wondering if someone could help me with this. Say we let ${B}({R})=\sigma(\{(a,b]:a be the Borel field of ${R}$.

If we let ${P},{Q}:{B}({R})\rightarrow[0,1]$ be probability measures. How does one prove or disprove that if ${P}((a,\infty))={Q}((a,\infty))$ for all ${a}\in{R}$ then ${P}({B})={Q}({B})$ for all ${B}\in{B}({R})$?

Do you know Dynkin's theorem that states that if two sigma-finite measures are equal for any element of a $\pi$-system that generates a sigma-algebra, then they're equal for any element of that sigma-algebra ?