[FOM] Transfinite Recursion in Functional Analysis and Measure Theory

Roger A. PURVES roger at stat.berkeley.edu
Thu Jan 31 21:02:21 EST 2019

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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