Kolmogov's book is a rather good one for the first reading. It's much more easier. Partially because Kolmogorov considered normed vector spaces. Normed vector spaces is rather simplier to imagine. And "imagination is more important than knowledge". Of course, one can learn to imagine abstract topological spaces. But I believe he cound not do it without understanding more easier theories.
Education is spiral. Let's explain what I mean. I learned the whole physics at school. I builded the whole world picture in school. I moved in a circle around the start point (the point of total ignorance). But what happened then? I entered to a university and started to learn physics from the mechanics. I learned the same domain of physics but more deeply. It was the second circle.
I think Kolmogorov's book is the first circle of an exciting travel through fuctional analysis
Thursday, April 19, 2007
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