This thesis is about measure and integration theory on Banachspaces,
especially about translation invariant measures. First, product measure son
initiate dimensional spaces are discussed. Afterward sit will be shown,
that, apart from some trivial examples, no measures exist bearing
properties such as (quasi-) translation invariance or σ-ﬁniteness. Then
the term zero set will be discussed and an adaptation of the term
originating from B. Hunt will be introduced, the new sets being called shy
sets. Afterwards, using this deﬁnition of zero sets, an σ-ﬁnite,
locally ﬁnite measure will be constructed which, althougn not being
invariant towards all zero sets, is translation invariant towards all schy
sets. Finally, the results will be displayed via several examples.