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- naming convention for "functional variance"

For a continuous function f:[a,b]-->R there is a well-known notion of "functional mean"

$$

\mu[f] = \frac{1}{b-a}\int_a^bf(x)\,dx.

$$

I am wondering if there is a name for the corresponding notion of "functional variance", i.e. the quantity

$$

\frac{1}{b-a}\int_a^b(f(x)-\mu[f])^2\,dx.

$$

?? Thanks. Also, does this quantity play a role somewhere in the literature? I'm writing a paper that involves this thing but google is very useless at answering my question since it just spits out pages upon pages about the variance of a continuous random variable.

$$

\mu[f] = \frac{1}{b-a}\int_a^bf(x)\,dx.

$$

I am wondering if there is a name for the corresponding notion of "functional variance", i.e. the quantity

$$

\frac{1}{b-a}\int_a^b(f(x)-\mu[f])^2\,dx.

$$

?? Thanks. Also, does this quantity play a role somewhere in the literature? I'm writing a paper that involves this thing but google is very useless at answering my question since it just spits out pages upon pages about the variance of a continuous random variable.

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