  The probabilistic investigation on record values and record times of a
sequence of random variables defined on the same probability space has received
much attention from 1952 to now. A great deal of such theory focused on
\textit{iid} or independent real-valued random variables. There exists a few
results for real-valued dependent random variables. Some papers deal also with
multivariate random variables. But a large theory regarding vectors and
dependent data has yet to be done. In preparation of that, the probability laws
of records are investigated here, without any assumption on the dependence
structure. The results are extended sequences with values in partially ordered
spaces whose order is compatible with measurability. The general
characterizations are checked in known cases mostly for \textit{iid} sequences.
The frame is ready for undertaking a vast study of records theory in high
dimensions and for types of dependence.
