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Math Help - Borel Fields

  1. #1
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    Borel Fields

    Hi, I was wondering if someone could help me with this. Say we let {B}({R})=\sigma(\{(a,b]:a<b\}) 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})?

    Any advice will be great.
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  2. #2
    Moo
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    Hello,

    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 ?
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