Nonstandard analysis, developed by Abraham Robinson, assigns infinitesimal but non-zero probabilities to individual points in continuous distributions, dissolving the tension without restricting additivity.

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Abraham Robinson(the subject of the statement): A 20th-century mathematician who invented a new way of working with infinitely small numbers (called non-standard analysis), making ideas that philosophers like Leibniz had about infinitesimals mathematically rigorous.
Continuous distributions(the mathematical structure being analyzed): A way of describing how something (like height or temperature) is spread out across a range of values with no gaps—think of all real numbers between 0 and 1.
additivity(Kolmogorov Axiom; breaks down at subatomic/quantum level): A property shared between probability measures and the concept of information, which holds at the macroscopic level but loses validity at the subatomic level in favor of a more subtle notion
infinitesimal(Nonstandard analysis): A hyperreal a whose absolute value |a| is less than 1/(n+1) for every natural number n

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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

Nonstandard analysis, developed by Abraham Robinson, assigns infinitesimal but non-zero probabilities to individual points in continuous distributions, dissolving the tension without restricting additivity.

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