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I want to read the topic "spaces of probability measures on a Polish space and the convergence". What is the best reference for that ?

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  • $\begingroup$ see the two references cited in math.stackexchange.com/q/607924/25917 $\endgroup$
    – BS.
    Commented Jan 8, 2015 at 16:28
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    $\begingroup$ billingsley and kurtz-ethier are the standard references. $\endgroup$
    – ofer zeitouni
    Commented Jan 8, 2015 at 17:55

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In addition to the "canonical" references mentioned above, the book "A Basic Course in Probability Theory" by Bhattacharya and Waymire has a very nice treatment of this topic in Chapter 5.

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Converting Ofer Zeitouni's comment to an answer:

  • Billingsley, Patrick. Convergence of Probability Measures.

  • Ethier, Stewart and Kurtz, Thomas. Markov Processes: Characterization and Convergence.

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