Math & Science ⇒ What is an operator (\operatorname{…}) and what is not

[yoblanco]

My question is about when should I use upright roman

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\operatorname{blah}

or in the whole document with

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\DeclareMathOperator{\foo}{blah}

to 'name' a function.

Here's an example, I hope you can tell me how do you decide what goes upright (as an operator) and what keeps italic:

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$\displaystyle \int f(x) \, dx \quad d(x,y) \quad \operatorname{d}(x,y) \quad \mathit{Var}(x) \quad \operatorname{Var}(x) \quad P(X=x) \quad \operatorname{P}(X=x) \quad E[X] \quad \operatorname{E}[X] \quad \mathit{Bin}(n,p) \quad \operatorname{Bin}(n,p) \quad B(\ell,\varepsilon) \quad \operatorname{B}(\ell,\varepsilon) \quad O(x) \quad \operatorname{O}(x)
$

d(x,y) means the distance, Var the variance of a distribution, P the probability, E the average (or mean of a distribution), Bin the binomial distribution, B the ball with center l and radius epsilon, O the http://en.wikipedia.org/wiki/Big_O_notation.

Which is the correct way to typeset all this function/operators? What is what we call operator in LaTeX? Any convincing law or rule to choose if writing as an operator (upright) or leave it italic?

Thank you in advance.

[cgnieder]

This isn't really a LaTeX question but a question of definition and (typographical) mathematical conventions. Maybe you'll find some insight in mathematics into type.

Regards

[yoblanco]

Good book, but it only say that one should know what goes upright and what doesn't. May be it's not absolute LaTeX related, but I think the question what does LaTeX understands as math operator? is related, and someone can add extra info about what should and what shouldn't be an operator.

Thank you for your answer.