  Shafer and Vovk introduce in their book \cite{ShaferVovk:2018} the notion of
\emph{instant enforcement} and \emph{instantly blockable} properties. However,
they do not associate these notions with any outer measure, unlike what Vovk
did in the case of sets of ''typical'' price paths. In this paper we introduce
an outer measure on the space $[0, +\ns) \times \Omega$ which assigns zero
value exactly to those sets (properties) of pairs of time $t$ and an elementary
event $\omega$ which are instantly blockable. Next, for a slightly modified
measure, we prove It\^o's isometry and BDG inequalities, and then use them to
define an It\^o-type integral. Additionally, we prove few properties for the
quadratic variation of model-free, continuous martingales, which hold with
instant enforcement.
