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		function is fed to the scientist in canonical order. Also observe that the auc measure is defined for a scientist on a function if the scientist converges on the function; it does not matter to what the scientist converges.

		Show that auc satisfies the axioms given in in Definition 12.10.

		This measure is developed in greater detail in Daley and Smith [54].

		12-7 (Freivolds [61], Kinber [106]) The following provides the function analog of the TxtMin paradigm.

		12.27 Definition

		(a) We say that M Min y -identifies f (written: ) just in case .

		(b) .

		Show that there is an acceptable programming system  y  for which Min y  has an infinite r.e. class of functions as an element.

		12-8 (Freivolds [61]) Freivolds introduced the notion of limit standardizability with a recursive estimate (abbreviated: Lsr) defined below:

		12.28 Definition We say that S is limiting standardizable via g with recursive estimate v (written: ) if and only if, for each , there is an if with  j if = f such that, for every i with  j i = f we have:

		(a) , and

		(b) .

		We say that S is limiting standardizable with a recursive estimate (written: ) if and only if, for some recursive g and v, .

		(a) Prove that the notion of Lsr is independent of the choice of an acceptable programming system.

		(b) Establish the following characterization of Min y -identification. The following are equivalent for allS.

		(i) For some acceptable  y , .

		(ii) .