On Application of Gaussian Measure

Key Points

• This research explores the implications of De Finetti's theorem on exchangeable probabilities in specific topological spaces.
• Analyzed De Finetti’s theorem in the context of standard spaces isomorphic to Borel subsets of the unit interval.
• Examined the validity of Dubins and Freedman's results in separable, metrizable spaces.
• Demonstrated that results by Dubins and Freedman may not hold in separable, metrizable spaces, indicating potential limitations of their findings.