null set

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a set that is empty

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x]} for which there exists more than one linear and continuous functional x* [member of] X* that satisfies <x*, x> = [parallel]x[parallel] and [parallel]x*[parallel] = 1 has no interior; if in addition, X is finite dimensional, this set has Lebesgue measure zero.
If, in addition, dimX < [infinity], then a classical Fubini theorem allows one to conclude that Z is of Lebesgue measure zero.
Thus it follows that G is of measure zero if and only [?
Moreover, a deeper analysis of this simple model reveals that the space of reduced form parameters divides into three sets, a set of positive measure on which the model is locally identified but not globally identified, a set of positive measure on which there is no representation of structural parameters satisfying the restrictions implied by (10), and a set of measure zero on which the model is globally identified.
The third set has measure zero on which every element has a unique structural representation that satisfies the restrictions.
On the other hand, the set of structural parameters that are globally identified is of measure zero because the constraint [b.
The set G, defined by (9), contains all such locally unidentified points but has measure zero according to Theorems 6 and 8.
In this appendix, we highlight a few properties of differentiable manifolds and develop some results about measure zero subsets of differentiable manifolds.
We exploit this local Euclidean structure to characterizer sets of measure zero on manifolds.
While measure zero sets are often studied in the context of Lebesgue measure, for Euclidean spaces we do not need the full power of this machinery.
k] is of measure zero if and only if for every [epsilon] > 0 there exist countably many closed k-dimensional rectangles [R.
The first arises because all results using the measure theoretic basis for probability have measure zero exclusion clauses.
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