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March 14

Names of these functions

Are there special names for functions that are of the form $1/(1+x^{2n})$ ? --HappyCamper 05:11, 14 March 2012 (UTC)[reply]

These functions are all rational functions, but not all rational functions are of the above form. There is no special name for the functions

f_{n}(x)=1/(1+x^{2n})

, nor should there be, because the sum or product of such functions is not of the same form. Why do you need a name? Bo Jacoby (talk) 13:46, 14 March 2012 (UTC).[reply]

If you google 1/(1+x^2n) you'll get a youtube video about the integral of that function as first result. Weird that google is smart enough to find that one despite it having the 2n in brackets, but not one of the other search results seems to match... 84.197.178.75 (talk) 14:57, 14 March 2012 (UTC)[reply]

Intuitive interpretation of Lebesgue integrals

Please see 1, 2 and 3. Which image is wrong? --151.75.123.9 (talk) 12:47, 14 March 2012 (UTC)[reply]

The third link is wrong (I have reverted that edit). One way to define the Lebesgue integral is to divide the range horizontally and then calculate the area under the resulting simple function. That's what the image was supposed to convey. Sławomir Biały (talk) 12:55, 14 March 2012 (UTC)[reply]

Also, the text beside the image explains this point. Sławomir Biały (talk) 12:57, 14 March 2012 (UTC)[reply]

Pls have a look here: Wikipedia talk:WikiProject Mathematics#Lebesgue_integration. I totally disagree to Slawomir.--Svebert (talk) 10:02, 19 March 2012 (UTC)[reply]