Sanika Ahmed, from Southsea, Hampshire, has Erb's palsy and needed surgery on her arm by the age of nine months.
BBC: Baby Sanika Ahmed's arm surgery legal fight over
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The compensation, approved by Mr Justice Foskett, is thought to be one of the highest amounts yet given for Erb's Palsy.
BBC: Barnet and Chase Farm Hospital
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"This continued steady increase...certainly is a testament to the long-standing stellar reputation of the New York City private and independent schools, " said ERB's executive director, Antoinette DeLuca.