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Lebesgue measure
Добавлено: 08 июн 2008, 14:20
Draeden
Lebesgue measure
Добавлено: 08 июн 2008, 14:59
Gaudeamus
? M - измеримое мн-во
Lebesgue measure
Добавлено: 08 июн 2008, 15:11
Draeden
Since
assume
and prove that
.
As
and
we can write, that
, but the last one has small measure:
.
That results in
.
Therefore, it's proved that
, but
i.e.
.
Q.E.D.
Lebesgue measure
Добавлено: 08 июн 2008, 15:39
Gaudeamus
As I understand,
depends on
.
Lebesgue measure
Добавлено: 08 июн 2008, 15:43
Draeden
You're right. You'd like a proof of lebesgue measurability without that ?
Lebesgue measure
Добавлено: 08 июн 2008, 15:55
Gaudeamus
I think it's not correct. You look over only one
Lebesgue measure
Добавлено: 09 июн 2008, 12:52
Draeden
therefore
it's clearly, that
is countable.
Lebesgue measure
Добавлено: 11 июн 2008, 06:34
Draeden
Lebesgue measure
Добавлено: 11 июн 2008, 06:53
Draeden
Integral then, if
Im a > 0, the integral equals to
if
Im a < 0, the integral is zero ( since
)
and, at last, if
Im a changes its sign while approaching to
0, the limit doesn't exist.
where's mistake ?
Lebesgue measure
Добавлено: 11 июн 2008, 08:07
Gaudeamus
Док-во вроде правильное.
Ha счет интеграла - поясни 2-e равенство.