Lebesgue Measure Flashcards
1
Q
If A is in B, both measurable, then…
L(B-A) = …
(L is lebesgue measure)
A
L(B) - L(A)
2
Q
If u is a finite measure on X,
E is measurable means…
A
u*(X) = u*(E) + u*(Ec)
(finite measure = u*(X) < ∞)
3
Q
E in R is lebesgue measurable
if and only if
A
there exists open sets O in R,
with E in O, where
L(O - E) < epsilon
“approximate from above”
4
Q
u a measure on Borel sets of X, a Hausdorff space
is a regular borel measure if…
A
1) u(k) < ∞ if K is compact
2) For a borel set B,
u(B) = inf {u(O) | O is open and B is in O}
“borel is open from above”
3) If O is open, u(O) = sup {u(K) | K is compact and K is in O}
“open is compact from below”
5
Q
any translation invariant regular borel measure on R is…
A
c*L
a contanst time lebesgue
6
Q
L, lebesgue measure
A
is a regular borel measure
