  H-measures and semiclassical (Wigner) measures were introduced in earlyn
1990s and since then they have found numerous applications in problems
involving $\mathrm{L}^2$ weakly converging sequences. Although they are similar
objects, neither of them is a generalisation of the other, the fundamental
difference between them being the fact that semiclassical measures have a
characteristic length, while H-measures have none. Recently introduced objects,
the one-scale H-measures, generalise both of them, thus encompassing properties
of both.
  The main aim of this paper is to fully develop this theory to the
$\mathrm{L}^p$ setting, $p\in(1,\infty)$, by constructing one-scale
H-distributions, a generalisation of one-scale H-measures and, at the same
time, of H-distributions, a generalisation of H-measures to the $\mathrm{L}^p$
setting, without any characteristic length. We also address an alternative
approach to $\mathrm{L}^p$ extension of semiclassical measures via the Wigner
transform, introducing new type of objects (semiclassical distributions).
Furthermore, we derive a localisation principle in a rather general form,
suitable for problems with a characteristic length, as well as those without a
specific characteristic length, providing some applications.
