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JoshuaZ comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

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Comment author: JoshuaZ 17 January 2011 05:12:14PM 0 points [-]

I'm not sure why you consider the gauge integral to be easier to understand the Lebesgue integral. It may be due to learning Lebesgue first, but I find it much more intuitive.

Also:

Royden is slightly better in this respect. The first four chapters are excellent, but still probably too theoretical. Further, eventually one will encounter measure spaces that aren't based on the real numbers and the Lebesgue measure,

Yes, this is a good thing. One doesn't understand a structure until one understands which parts of a structure are forcing which properties. Moreover, this supplies useful counterexamples that helps one understand what sort of things one necessarily will need to invoke if one wants certain results.

Comment author: Will_Sawin 17 January 2011 08:53:46PM 3 points [-]

It is much easier to understand what the words in the definition of the gauge integral mean. It is harder to understand why they are there.

Comment deleted 18 January 2011 06:23:02AM [-]
Comment author: JoshuaZ 18 January 2011 02:48:14PM 0 points [-]

Yes, I did make it to the end of the sentence. But I misinterpreted the sentence to be having two distinct criticisms when there was only one.