## 2.5 Chaotic distributions

**Definition
2.5.1:** A distribution of an attribute is **totally chaotic**
if the assignment relations do not have any invariance domain, and
the domain of the distributed and of the support attribute are
continuous and infinite.

Comment
2.5.1: The distribution type was not mentioned any more in definition
2.5.1 (primary or derived distribution) because the definition is
valid for both distributions types. When only the “distribution”
term shall be used next in this paper, this means that any of its
types are self-understood.

According to the definition 2.5.1, a
totally chaotic distribution is a particular case of distribution,
where there is not a single continuity interval across the entire
support domain, __for the assignment relations__, the allotted
values being totally random. The totally chaotic distributions may be
also probabilistically defined, which means that these are the
distributions at which the density of occurrence probability of any
value is even (equiprobable values). After all the facts which have
been aforementioned in this paper, it is obvious that the totally
chaotic distributions are virtual objects, used in mathematics field,
but unable to be realized. If the values domain of the distributed
and support attribute is limited (finite and known), made-up from a
finite number of normal singular values, then the distribution is
only *partial chaotic* (that is the case of realizable chaotic
distributions) and that is due to the fact that any restriction on a
domain of values means a information amount growth, as we are about
to see in chapter 8 and 9. In case of the totally chaotic
distributions, the inner information amount associated to them is
null.

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