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 Post subject: Product of two absolutely continuous functionPosted: Sun, 6 Nov 2005 20:19:43 UTC
 Senior Member

Joined: Fri, 22 Oct 2004 22:59:11 UTC
Posts: 74
I'm trying to show that the product of two absolutely continuous functions is absolutely continuous.

This is what I've tried: Since if a function is absolutely cont. means that it is a function of bounded variation on some interval [a,b].
so, I've been trying to show that the product of two functions of bounded variation is also of bounded variation... Is this the right idea?

Any help is greatly appreciated

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 Post subject: Posted: Mon, 7 Nov 2005 05:11:30 UTC
 Senior Member

Joined: Fri, 22 Oct 2004 22:59:11 UTC
Posts: 74
got it!
pretty simple actually. I was on the right track, just consider the function of bounded variation. Then, use the standard continuity trick of adding a term, triangle it, then just take the sum over the index of the partition.

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