Comment on Money pumping: the axiomatic approach

Mon, 09 Nov 2009 19:19:03 GMT

Correct, by definition, if you have a dense set (which by default we treat the probability space as) and we map it into another space than either that space is also dense, in which case the converging sequences will have limits or it will not be dense (in which case continuity fails). In the former case, continuity reduces to point-wise continuity.

Note, setting the limit to "no preference" does not resolve the discontinuity. But by intermediate value, there will exist at least one such point in any continuous approximation of the discontinuous function.

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