measurable set वाक्य

In general they are much more complicated than generator sets, but much better than non-measurable sets.
where the supremum is taken over all partitions " \ pi " of a measurable set"
These subsets will be called the measurable sets.
The notion of a non-measurable set has been a source of great controversy since its introduction.
In contrast, an example of a non-measurable set cannot be exhibited, though its existence can be proved.

Striving to get rid of null sets, mathematicians often use equivalence classes of measurable sets or functions.
Suppose is a measurable set and is a nondecreasing sequence of non-negative measurable functions on such that
Each measurable set has associated a non-negative real number called its measure ( generalizes the notion of'area'and'volume').
There is, however, an important difference between the two : the Banach Tarski paradox relies on non-measurable sets.
*So long as there are non-measurable sets in a measure space, there are non-measurable functions from that space.