It is shown that the standard Kolmogorov model for probability spaces cannot in general allow the elimination but of only a small amount of probabilistic redundancy. This issue, a purely theoretical weakness, not necessarily related to empirical reality, appears not to have received enough attention in foundational studies of Probability Theory. 1. The Need for a Match Several recent works have brought to attention the events during the first decades of the 20th century which culminated in 1933 with Kolmogorov’s foundation of modern Probability Theory in his Grundbegriffe, see Shafer & Vovk , Vovk & Shafer, von Plato, or Bilova et.al. Ever since Probability Theory first started to emerge in the work of Jacob Bernoulli early in the 18th century, there has been an interest in the extent to which such a theory may in fact match with the empirical reality it is supposed to model. The axiom regarding ”total probability”, namel
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.