Non-uniqueness of hyperreal extensions means infinitely many incompatible regular hyperreal probability functions exist for the same sample space, making regularity indeterminate rather than preserved.
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Regularity (in probability)(in formal probability theory)
A property where every possible outcome in a probability system has some non-zero chance of occurring—nothing is completely impossible.
Sample space(a mathematical concept needed to make fair comparisons)
In probability and statistics, the complete set of all possible outcomes you're considering; for example, the sample space for a coin flip is 'heads' or 'tails'.
incompatible(as used to describe conflicting demands or responsibilities)
Unable to exist or work together at the same time; conflicting with each other.