Effective weak convergence and tightness of measures in computable Polish spaces

Prokhorov's Theorem in probability theory states that a family $\Gamma$ of probability measures on a Polish space is tight if and only if every sequence in $\Gamma$ has a weakly convergent subsequence. Due to the highly non-constructive nature of (relative) sequential compactness, however, the effective content of this theorem has not been studied. To this end, we generalize the effective notions of weak convergence of measures on the real line due to McNicholl and Rojas to computable Polish spaces. Then, we introduce an effective notion of tightness for families of measures on computable Polish spaces. Finally, we prove an effective version of Prokhorov's Theorem for computable sequences of probability measures.

• Publication year

  2024

• Venue

  arXiv.org

• Publication date

  2024-10-28

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.48550/arXiv.2410.21609arXiv 2410.21609
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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