  We present three methods to construct majorizing measures in various
settings. These methods are based on direct constructions of increasing
sequences of partitions through a simple exhaustion procedure rather than on
the construction of well separated ultrametric subspaces. The first scheme of
construction provides a simple unified proof of the Majorizing Measure Theorem
for Gaussian processes and of the following fact. If $A,B$ are balanced convex
sets in a vector space, and if $A$ is sufficiently convex, a control of the
covering numbers $N(A,\varepsilon B)$ for all $\varepsilon>0$ implies the (a
priori stronger) existence of a majorizing measure on $A$ provided with the
distance induced by $B$. This establishes, apparently for the first time, a
clear link between geometry and majorizing measures, and generalizes the
earlier results on majorizing measures on ellipsoids in Hilbert space, that
were obtained by specific methods. Much of the rest of the paper is concerned
with the structure of bounded Bernoulli (=Radmacher) processes. The main
conjecture on their structure is reformulated in several ways, that are shown
to be equivalent, and to be equivalent to the existence of certain majorizing
measures. Two schemes of construction of majorizing measures related to this
problem are presented. One allows to describe Bernoulli processes when the
index set, provided with the supremum norm, is sufficiently small. The other
allows to prove a weak form of the main conjecture.
