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(b) Consider an M such that for each s, M( s ) = p s where, for all x,  . |
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Show that M Ap-identifies each member of  . |
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7-11 Fulk and Jain [73] define the following density-restricted version of the Ap criterion (see Exercise 7-10). For each  , we say that M Dapa-identifies f (written:  ) if and only if there is a sequence  of subsets of N that satisfy (i) through (iv) as in Exercise 7-10 and (v)  . For each  , define Dapa(M) and Dapa as usual. |
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(a) Show that for each  ,  . (Hint:: Use an operator recursion theorem argument.) Thus, while the Ap criterion is independent of encodings of experiments (unlike the Aex criteria), the Ap criterion has serious difficulties with density. |
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(b) Show that for each a and b with  ,  . |
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