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Functions : L-Spaces ( Lebesgue Spaces )

Consider the following function:

f(x) = 1/x for x in [1, infinity)
= 1 for x in (-1,1)
= -1/x for x in (-infinity, -1]

Please explain why f(x) is in L^2(R)L^1(R)

Solution Summary

L-spaces are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.