Random sequence convergence theorem

Hi all,

I have the following problem. Let Xn and Yn be random sequences both
converging to 0 in probability.Let Xn be independent of Yn for each n
and Xn-Yn converges to 0 almost surely.Is it true that Xn converges to
0 almost surely?

Please if have any idea share to me.

Greetings Mladen

.

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