Nuprl Definition : separable-kernel
separable-kernel(rv;e;f) ==
∃phi:ℝ ⟶ ℝ. ∃psi:{h:Point| h ⋅ e = r0} ⟶ ℝ. ∀h:{h:Point| h ⋅ e = r0} . ∀t:ℝ. ((f h t) = ((phi t) * (psi h)))
Definitions occuring in Statement :
rv-ip: x ⋅ y,
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
ss-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n
Definitions occuring in definition :
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
set: {x:A| B[x]} ,
ss-point: Point,
rv-ip: x ⋅ y,
int-to-real: r(n),
natural_number: $n,
all: ∀x:A. B[x],
real: ℝ,
req: x = y,
rmul: a * b,
apply: f a
FDL editor aliases :
separable-kernel
Latex:
separable-kernel(rv;e;f) ==
\mexists{}phi:\mBbbR{} {}\mrightarrow{} \mBbbR{}
\mexists{}psi:\{h:Point| h \mcdot{} e = r0\} {}\mrightarrow{} \mBbbR{}. \mforall{}h:\{h:Point| h \mcdot{} e = r0\} . \mforall{}t:\mBbbR{}. ((f h t) = ((phi t) * (psi h)\000C))
Date html generated:
2017_10_05-AM-00_23_37
Last ObjectModification:
2017_07_01-PM-09_15_04
Theory : inner!product!spaces
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