Manuscript IX-E-3@1 · IX-E-3.tex · section · 8c41417a

Actual ordering and derivative support

Copied inputs and conventions › Actual ordering and derivative support · lines 406–435

IX-E-3@1#eq:ordering, IX-E-3@1#eq:SB

The series definition is

F_{1} ≳ F_{2} ⟺ supp_{fun} F_{1} \cap J^{-} (supp_{fun} F_{2}) = \emptyset .

Null relation and coincidence are included. Two-way ordering means that both orderings hold.

We use IX-E-2's derivative-support characterization: on the unrestricted affine configuration space, functional support is the closure of the union of the supports of all first-derivative distributions, over all configurations and field components. This characterization is an imported result, not a replacement by the upper set in (eq:upper) IXE2.

The obligation is

B_{f} ≳ W_{g}, W_{g} ≳ B_{f} ⟹ f (x) g (y) Im K (x, y) = 0.

Displayed formulas in this passage

IX-E-3@1#eq:ordering · line 409
$F_{1} ≳ F_{2} ⟺ supp_{fun} F_{1} \cap J^{-} (supp_{fun} F_{2}) = \emptyset .$
IX-E-3@1#eq:SB · line 426
$B_{f} ≳ W_{g}, W_{g} ≳ B_{f} ⟹ f (x) g (y) Im K (x, y) = 0.$