The paper is devoted to the concept of conical measures which is central for the Choquet theory of integral representation in its final version. The conical measures need not be continuous under monotone pointwise convergence of sequences on the lattice subspace of functions which form their domain. We prove that they indeed become continuous (even in the nonsequential sense) when one restricts that domain to an obvious subcone. This result is in accord with the recent representation theory in measure and integration developed by the author. We also prove that one can pass from the subcone in question to a certain natural extended cone.
KeywordsIntegral Representation Representation Theory Final Version Recent Representation Lattice Subspace
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