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The Bessel point process is a rigid point process on the positive real lineand its conditional measure on a bounded interval $[0,R]$ is almost surely anorthogonal polynomial ensemble. In this article, we show that if $R$ tends toinfinity, one almost surely recovers the Bessel point process. In fact, we showthis convergence for a deterministic class of probability measures, to whichthe conditional measure of the Bessel point process almost surely belongs.

Universality for conditional measures of the Bessel point process