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A theorem of C. Bayer and J. Teichmann implies that if a finite real multisequence b b (2d) has a representing measure, then the associated mo- ment matrix Md admits positive, recursively generated moment matrix exten- sions Md+1, Md+2, . . .. For a bivariate recursively determinate Md, we show that the existence of positive, recursively generated extensions Md+1, . . . , M2d 1 is sufficient for a measure; examples illustrate that all of these exten- sions may be required. We describe in detail a constructive procedure for de- termining whether such extensions exist. Under mild additional hypotheses, we show that Md admits an extension Md+1 which has many of the properties of a positive, recursively generated extension.

Recursively determined representing measures for bivariate truncated moment sequences