B****n
发帖数: 11290 | 1 1. Please give an example of a subset of [0,1] with outer measure 1 and inner
measure 0. (Use traditional lebesgue measure)
2. Please give an example that a sequence of arbitrary maps Tn:[0,1]->R is
decreasing to 0, |Tn|<=1 for all n, and E*Tn=1 where E*Tn is the outer
integral defined by inf{EU, U measureable and larger than Tn EU exists}' Here
is also lebesgue measure on [0,1].
This question is a about counter example of dominated convergence theorem for
arbitrary non-measurable maps with orin | f****t
发帖数: 101 | 2 o, you practise yourself for homework a.
【在 B****n 的大作中提到】
: 1. Please give an example of a subset of [0,1] with outer measure 1 and inner
: measure 0. (Use traditional lebesgue measure)
: 2. Please give an example that a sequence of arbitrary maps Tn:[0,1]->R is
: decreasing to 0, |Tn|<=1 for all n, and E*Tn=1 where E*Tn is the outer
: integral defined by inf{EU, U measureable and larger than Tn EU exists}' Here
: is also lebesgue measure on [0,1].
: This question is a about counter example of dominated convergence theorem for
: arbitrary non-measurable maps with orin
| f****t
发帖数: 101 | 3 o, you practise yourself for homework a.
【在 B****n 的大作中提到】
: 1. Please give an example of a subset of [0,1] with outer measure 1 and inner
: measure 0. (Use traditional lebesgue measure)
: 2. Please give an example that a sequence of arbitrary maps Tn:[0,1]->R is
: decreasing to 0, |Tn|<=1 for all n, and E*Tn=1 where E*Tn is the outer
: integral defined by inf{EU, U measureable and larger than Tn EU exists}' Here
: is also lebesgue measure on [0,1].
: This question is a about counter example of dominated convergence theorem for
: arbitrary non-measurable maps with orin
|
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