Is there a difference between these two terminologies?
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space of all Borel probability measure on $\mathbb R^n$ or some complete, separable metric space.
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space of all Probability measure on $\mathbb R^n$ or some complete, separable metric space.
In other words, what would be differences in the definitions of a Borel probability measure and a probability measure on the above mentioned spaces.
Thanks for explaining to me.
Best Answer
In 2) the sigma-algebra is not specified.
In 1) the sigma-algebra is the sigma-algebra of all Borel sets, the one generated by open sets.