Summary.
We apply a version of the Strassen–Dudley theorem for Markov kernels to obtain a strong approximation theorem for sequences of random variables with values in Polish spaces. The conditions are expressed in terms of the Prohorov distance of regular conditional distributions. By avoiding discrete approximation of the random variables we can improve the upper bounds for the approximation.
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Received: 21 June 1994 / In revised form: 3 April 1996
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Römersperger, M. A note on nearby variables with nearby conditional laws. Probab Theory Relat Fields 106, 371–377 (1996). https://doi.org/10.1007/s004400050069
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DOI: https://doi.org/10.1007/s004400050069