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[tex]f:\mathbb{R}^n\to\mathbb{R}[/tex]

we havederivatives

[tex]

\frac{\partial}{\partial x_k} f,

[/tex]

and for functionals

[tex]

F:\mathcal{H}\to\mathbb{R},\quad\quad\quad \mathcal{H}\subset \mathbb{R}^{\mathbb{R}^n}

[/tex]

we havefunctional derivatives

[tex]

\frac{\delta}{\delta f(x)} F.

[/tex]

But if we have a linear form defined on a space of functionals,

[tex]

\mathcal{F}:\mathcal{Z}\to\mathbb{R},\quad\quad\quad \mathcal{Z}\subset \mathbb{R}^{\mathcal{H}},

[/tex]

then what's the name for this

[tex]

\frac{\mathcal{D}}{\mathcal{D} F(f)} \mathcal{F}?

[/tex]

Did I manage giving it a logical notation at least? In any case, I have no idea what it should be called.

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# Extremely infinite dimensional calculus

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