This sum was reduced on appeal to £40,000 – but McDonald's never enforced payment.
The lawsuit, filed in New York State Supreme Court, originally sought $25 million in damages on the grounds of defamation and gender discrimination; it was later narrowed to gender discrimination and the sum was reduced to $13 million.
The footballer was awarded damages of £80,00, but that sum was reduced on appeal to £1 and Grobbelaar was ordered to pay NGN's legal costs, which totalled several hundred thousand pounds.
By Lemma 7 we can assume that the sum is reduced.
Let (Omega '=Omega {setminus }Omega _{max}.) Then (a=sum nolimits _{iin Omega '} a_i) and this sum is reduced.
The resulting sum is reduced by following similar procedures to the ones mentioned in the first item.
For an arbitrary nonzero converging sum (a=sum nolimits _{iin Omega } a_i,, a_iin L(Gamma ),) there exists a nonempty subset (Omega 'subset Omega ) such that (a=sum nolimits _{iin Omega '} a_i) and this sum is reduced.
Clearly, it is a topological basis in ({widehat{M}}_{infty }(F).) We will need another general statement about sums in ({widehat{L}}(Gamma ).) Consider a nonzero converging sum (a=sum nolimits _{iin Omega } a_iin {widehat{L}}(Gamma ),, a_iin L(Gamma ).) We say that the sum is reduced if for any arbitrary nonempty subset (Omega 'subset Omega ) we have (sum nolimits _{iin Omega '} a_ine 0).
Finally, in the case where this sum is reduced to one element, which is the case for non-characteristic points, we use modulation theory coupled with a nonlinear argument to show the exponential convergence (in the self-similar time variable) of the various parameters and conclude the proof.
Rewriting each summand (p q^*, (p,q) in mathcal {P'} (p_0,q_0),) as a linear combination of basic elements from (B gamma )) and using Lemmas 5, 6 we get (a'=sum beta _{p,q}pq^*,) where (beta _{p,q}in F,,, l(p)=l q), s(p)=s q)=v, pq^* in B gamma )) for each summand and the sum is reduced.
The court ordered Telenor to pay compensation of $2.8 billion, a sum that was reduced to $1.7 billion on appeal.
