measurable function meaning in Hindi

Examples

1. Lebesgue's theory defines integrals for a class of functions called measurable functions.
2. As a result, the composition of Lebesgue-measurable functions need not be Lebesgue-measurable.
3. Integration theory defines integrability and integrals of measurable functions on a measure space.
4. The only information available is the basic properties of ?-algebras and measurable functions.
5. Extending to measurable functions is achieved by applying Riesz-Markov, as above.
6. It can be used to prove H�lder's inequality for measurable functions
7. Monotone convergence theorem : Suppose is a sequence of non-negative measurable functions such that
8. In general, the supremum of any countable family of measurable functions is also measurable.
9. This shows that Tonelli's theorem can fail for non-measurable functions.
10. These spaces are spaces of measurable functions on when, and of tempered distributions on when.