2.theprincipleofnestedintervals
1.thedefinitionofnestedintervals 3360
The set of intervals
whichhasthefollowingproperties :
1.)
2.)
iscalledthesystemofnestedintervals。
2.theprincipleofnestedintervals 3360
Suppose
isasetofintervalsthatsatisfiesthepropertiesabove。
i.e。
thentheprincipleofnestedintervalscanbewrittenasfollowingforms 3360
1.) For a system of nested intervals
The sequence
have the following property:
同调
Clearly，sequence
ismonotoneincreasingandeveryelementofsequence
is his upper bound. Sequence
ismonotonedecreasingandeveryelementof
is his lower bound。
bythemonotoneconvergencetheorem、
与
区域转换。
bythedefinitionofnestedintervals，we have:
同调
热
Suppose
亨斯，
2.) Then let's prove the uniqueness of
同调
supposethereisarealnumbersuchthat
. We want to prove
同调
Since
热
同调
Due to
因为，
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