First, we have to know that every set of positive measure contains a nonmeasurable subset.

A nonmeasurable set is considered null if it is a subset of a null measurable set.

"They downplay the kinds of things that can't be measured and shortchange the importance of nonmeasurable factors in human food like choice and taste.

Attempts to define probabilities for all subsets of the real numbers run into difficulties when one considers 'badly behaved' sets, such as those that are nonmeasurable.

Let be a set whose inner Lebesgue measure is equal to 0, but outer Lebesgue measure - to 1 (thus, is nonmeasurable to extreme).

However, this individual had radiographic lesions (pleural and bone metastases) that were deemed nonmeasurable by RECIST criteria.

But Dr. Laczkovich found that the trick is to cut the circle into what mathematicians call nonmeasurable pieces, that is, collections of points that are so irregular that they cannot be measured.

Martin Conroy, a professor of education and economics at Stanford University, said: "I'm worried that there are all sorts of nonmeasurable characteristics of these kids that made it difficult for them to get into these private schools.

Unlike full AC, DC is insufficient to prove (given ZF) that there is a nonmeasurable set of reals, or that there is a set of reals without the property of Baire or without the perfect set property.

It can be proven only by using the axiom of choice, which allows for the construction of nonmeasurable sets, i.e., collections of points that do not have a volume in the ordinary sense and that for their construction would require performing an uncountably infinite number of choices.

And this line of thought, which coincides with what may be called 'revived capitalism' , seeks to define standards of living by using criteria which are non-quantifiable and nonmeasurable, but which have an incidence on the welfare of the citizens. Sustainable development is one of these and has been emphasized by various groups.