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On Tue, 1 Aug 2006, Stephen Montgomery-Smith wrote:
Both these inequalities are the bread and butter of my research. They
are both great inequalities, but I use them so much that they have
become almost like 1+1=2 to me. I have been interested in extensions of
Jensen's inequality. The rearrangement inequality is fundamental to the
study of so called rearrangement invariant spaces, about which I have
many papers.
When you do math at your level -- stuff that has never been done before --
you must have to get to the point where many things that were once
difficult become automatic. How else could you "see" the big picture of
what you are working on? I think these inequalities are pretty simple
compared to a lot of other things that have become like 1+1=2 to you,
things I've never heard of before and wouldn't understand.
Mike
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