borel measure meaning in Hindi

Examples

1. Any measure defined on the Borel sets is called a Borel measure.
2. Without the condition of regularity the Borel measure need not be unique.
3. for some Borel measures \ mu _ i.
4. Furthermore, the Dirac delta function is not a function but it is a finite Borel measure.
5. If is a finite Borel measure on, then the Fourier Stieltjes transform of is the operator on defined by
6. For a Borel measure \ mu on a Euclidean space \ mathbb { R } ^ { n } define
7. By Carath�odory's extension theorem, there is a unique Borel measure on which agrees with on every interval.
8. In more abstract language, the theorem characterises Laplace transforms of positive Borel measures on [ 0,  " ).
9. This definition makes sense if " x " is an integrable function ( in distribution, or is a finite Borel measure.
10. The linear functional taking a continuous function to its value at ? corresponds to the regular Borel measure with a point mass at ?.