If each point receives a positive infinitesimal probability and hyperfinite summation is employed, full additivity is recoverable within a well-defined mathematical framework endorsed by Bernstein and Wattenberg (1969).
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nonstandard analysis(Built on the expressive strength (can formalize calculus) and expressive weakness (cannot rule out infinitesimals) of first-order logic)
Abraham Robinson's framework that uses the compactness theorem of first-order logic to construct a model R' elementarily equivalent to the real numbers R but containing infinitesimals, thereby giving rigorous foundations to Leibniz-style infinitesimal reasoning
probability(as used in mathematics and logic)
A number between 0 and 1 that describes how likely something is to happen; 0.5 means 50% chance, 1 means certain, 0 means impossible.