Nonstandard measure theory–Hausdorff measure

A nonstandard proof of a lemma from constructive measure theory

The conceptual gulf between constructive analysis (in the sense of Bishop [1]) and nonstandard analysis (in the sense of Robinson [7]) is vast, despite the historical genesis of both methodologies from foundational considerations. Those who use nonstandard arguments often say of their proofs that they are “constructive modulo an ultrafilter”; implicit in this statement is the suggestion that su...

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

Measure for Measure

Macro measurement is a long and arduous process that impinges upon the system of national accounts. The challenge it raises is driven by the demand of economic policy. In present time the need will arise with sustainable growth that mixes environmental concern and development policy. It calls for no less than a sea change in national accounting, from a system of income and expenditure accounts ...

Ranking of generalized fuzzy numbers using distance measure and similarity measure

embedding measure spaces

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...