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Jul 2018
For translational
          invariant functions              
         The Lebesgue measure is an            example of such a function;
                                                       ­   In geometry, a translation "slides"

a thing by a: Ta(p) = p + a.


           In physics and mathematics,
continuous translational symmetry
is the invariance of a system of
equations under any translation.
Discrete translational symmetry
    is invariant under discrete translation;

Analogously an operator A on functions
     is said to be translationally invariant
     with respect to a translation operator
{\display style T{\delta }} T{\delta }
if the result after applying A doesn't change
if the argument function is translated.
        More precisely it must hold that:

                {\display     style \for                       all \delta \
                                                         Af=A(T{\delta }f).\,}
                                                        \for    ­         all \delta \ Af=A(T
{\delta
                                                       }f).\,              
                                              Laws of physics are translationally invariant
                                          
    under a spatial translation
     if they do not distinguish
      different points in space.
                                 According to Noether's theorem,
    space translational symmetry of a physical system
      is equivalent to the momentum conservation law.

Translational symmetry of any woman
means that a particular translation does not change her.
         For a given woman, the translations
         for which this applies form a group,
         the symmetry group, or, if the women
         have more kinds of symmetry,                           a subgroup of the symmetry group.
Wikipedia
Johnny  Noiπ
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   Keith Wilson
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