- #1

- 970

- 3

## Main Question or Discussion Point

What's the point of defining [tex]\sigma [/tex] algebras, i.e., why must we assign measures only to elements of a [tex]\sigma [/tex] algebra?

Second, can you give an example of a set contained in the Lebesgue [tex]\sigma [/tex] algebra, but not the Borel [tex]\sigma [/tex] algebra? Also, is there a set not contained even in the Lebesgue [tex]\sigma [/tex] algebra?

Second, can you give an example of a set contained in the Lebesgue [tex]\sigma [/tex] algebra, but not the Borel [tex]\sigma [/tex] algebra? Also, is there a set not contained even in the Lebesgue [tex]\sigma [/tex] algebra?