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 Oct 5 revised I need to compute one integral in terms of another integral. edited tags Oct 5 revised I need to compute one integral in terms of another integral. added 3 characters in body Oct 5 comment I need to compute one integral in terms of another integral. ok, ok, ok....... Oct 5 revised I need to compute one integral in terms of another integral. added 115 characters in body Oct 5 asked I need to compute one integral in terms of another integral. Sep 16 comment is a direct sum of Hilbert spaces a Hilbert space.? But Wikipédia presents a condition that is not present on proofwiki: the sum of all norms for each function on the direct sum must converge. Sep 16 asked is a direct sum of Hilbert spaces a Hilbert space.? Sep 16 comment Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? Very good coment! However I would like to know why it is not an inner product, since it is linear in the first argument, positive definite, and symmetric. Sep 14 revised Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? added 64 characters in body Sep 14 comment Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? This is not the core of the question. Anyways, a nonlinear operator is an operator which does not have the superposition property. Sep 14 asked Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? Aug 23 awarded Scholar Aug 23 accepted A quasimetric for a space formed by nouns Aug 23 awarded Supporter Aug 23 comment A quasimetric for a space formed by nouns very good answer! actually you are representing "popularity" of the noun as a function that takes an article and returns some quantity related to the number of appearances of the noun in the article. About your pseudometric $d(x, y)$: if $x$ and $y$ are close related, then $d(x,y)$ is very close to $0$, which is really what I need. About the "pseudo": I can always construct the set $A$ such that, for all $x \in S$ there will exist an article $a \in A$ with $R(a) \cap S = \{x\}$. Therefore, under this restriction, $d(x,y)$ is a metric, which solves my problem. Aug 22 asked A doubt about tensor product on Hilbert Spaces Aug 22 awarded Student Aug 21 comment A quasimetric for a space formed by nouns Actually I don't want to measure similarity between strings. I want to measure similarity between string meanings. $A$ represents the set of all journal articles. Aug 21 comment A quasimetric for a space formed by nouns I have changed the problem definition to account for these doubts. Thank you for your answer. Aug 21 revised A quasimetric for a space formed by nouns added 16 characters in body