Bieber later arranged for the girl to meet him in New York, before he tweeted that the experience was inspiring and the best thing he's done.
Avalanna suffered from an atypical teratoid rhabdoid tumour. Only 30 new cases are diagnosed in the US each year.
Bieber mourned the death of "one of the greatest spirits i have ever known," saying in a tweet: "RIP Avalanna. i love you."He also posted a photo of himself with Avalanna, simply captioned "My angel".
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