The set A is called an Aronszajn
null set (or simply, a
null set) if
If [phi]([SIGMA]) [??] [SIGMA] and [mu]([phi](A)) = 0 for every
null set A [member of] [SIGMA], then W has Hyers-Ulam stability if and only if there exists a positive constant r such that [phi](U(r)) = [phi]([sigma](u)), where U(r) := {x [member of] X : |u(x)| [greater than or equal to] r}.
Here, N(r) - N(s) equals a
null set, which violates the rule of [[member of].sub.n]{n:n [member of] N(j) and n [not member of] N(i)}.
Danner acknowledges that missing middle, Which is in effect a
null set that includes the data we don't have.
This could have very easily ended up as a
null set: 1 + -1 = 0.
With the exception of the
null set that contains nothing, all other sets contain certain members/elements.
"We bought a virgin." For her role as a
null set, that's important.
Instead, a single access point would be used for all levels, and the data would be returned as requested, returned with modification, or simply returned as a
null set in which the user would think that simply no matches were made to the query sent.
He called these locations the "
null set" and they encompass the lower portion of the academic dimension.
Choosing priests and religious as coparents could be a key device if elite Florentines wished to emphasize marital strategies with social peers over baptismal kinship strategies with social peers.(29) In this case, a priest represented the
null set. Priests also formed the hub of a parish's wheel of gossip; they represented an excellent source for news.(30) Yet since Florentines feared that confession to their own parish priest meant that the local parish would hear about their sins, they saw advantage in establishing a relationship with a priest from a different parish.
Had the monotonicity assumptions not been correct, the likely result would have been
null sets for the feasible regions in the constrained estimation problems of Eqs.
Then, by [4, Remark 3.4], there exists [x.sup.*.sub.0] [member of] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that [absolute value of x * v] is a local control measure for v, that is, [absolute value of x * v] has the same
null sets as v.
