Editing Almost periodic function (section)

===Stepanov almost periodic functions===
The space ''S''<sup>''p''</sup> of Stepanov almost periodic functions (for ''p''&nbsp;≥&nbsp;1) was introduced by V.V. Stepanov (1925).<ref>W.  Stepanoff(=V.V. Stepanov),   "Sur quelques généralisations des fonctions presque périodiques"  C. R. Acad. Sci. Paris, 181  (1925)  pp.&nbsp;90–92; W.  Stepanoff(=V.V. Stepanov),   "Ueber einige Verallgemeinerungen der fastperiodischen Funktionen"  Math. Ann., 45  (1925)  pp.&nbsp;473–498</ref> It contains the space of Bohr almost periodic functions. It is the closure of the trigonometric polynomials under the norm

:<math>\|f\|_{S,r,p}=\sup_x \left({1\over r}\int_x^{x+r} |f(s)|^p \, ds\right)^{1/p}</math>

for any fixed positive value of ''r''; for different values of ''r'' these norms give the same topology and so the same space of almost periodic functions (though the norm on this space depends on the choice of&nbsp;''r'').