| 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 ?.
|
मोबाइल