# Hall's marriage theorem for infinite system of finite sets

We have proved the Hall's marriage theorem for the finite system of finite sets; now I would like to show that it holds even for infinite system of finite sets.

I have been trying to prove this myself for quite a while, but did not succeed. Can anyone provide a sketch of the proof?

Thanks a lot!

• Is the theorem known to be true for infinite systems of finite sets? – templatetypedef Sep 10 '13 at 22:31
• I suspect yes; but I am not sure. – Ondra Hrubý Sep 10 '13 at 22:34