[FOM] Transfinite Recursion in Functional Analysis and Measure Theory

[Roger A. PURVES]

L.E. Dubins and L.J Savage used transfinite recursion(*) to establish

the existence and uniqueness of extensions of a family of finitely

additive probability measures, provided a linear functional based on

the extensions satisfied a certain natural condition. This is Theorem

1 of Chapter 2 of their 1965 book "How to Gamble if You Must".



Roger Purves


(*) The recursion was based on the levels of what Dubins and Savage

referred to as the Kalmar hierarchy)
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