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dalo2m1ezyxlo

dalo2m1ezyxlo

Answered question

2022-06-02

Prove that lim n m = 1 f ( m , n ) m = 1 ( lim n f ( m , n ) )

Answer & Explanation

bapeSoypelp0vs

bapeSoypelp0vs

Beginner2022-06-03Added 4 answers

The statement is false. Consider
f ( m , n ) = { 1 n  if  n m < 2 n 0  otherwise.
Then m = 1 f ( m , n ) = 1 and lim n f ( m , n ) = 0 which turns your inequality into
1 0.
This function is an example of why non-negativity is an essential requirement of Fatou's lemma.

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