& b% i2 o4 V' c3 L: G X) J/ i - W. b( _9 Q+ W, F$ O HClass3 $ z4 e* M o# N3 y) s7 USec.1.2. Measure : Y$ d5 \% Y3 F! |7 D, f7 z6 {0 P8 n( X
Sec.1.3. Outer Measure 7 Z6 [8 D" k) G+ x % x$ W9 }$ F- [3 b7 g3 v( ]( t2 ]& G
Class4) x# @- J9 E& F* }$ {8 r- }% k# D8 O
Sec.1.4. Constructing outer measure- m, U6 `+ U7 z! `$ p' R
' G9 |/ u/ k3 W* w- D- j2 u4 g1 h
, ^& X7 J7 [- N* L/ DClass57 A: H7 F5 d( w+ `( [' d
Sec.1.5-1.6 Lebesgue measure" I+ ~+ u5 Y) r+ d+ ?
3 h6 {- W1 r3 B5 ~* I
& S" T( y. G! U/ t$ ]
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5 e3 {5 F3 S9 H. [5 u Z
Class7. B1 E2 V/ Y5 t3 W0 H! i
Sec.1.8-1.9 Construction of metric outer measure , t+ q. w# N2 c$ j- M / O* i2 e/ b; A/ u4 l- j' Y3 R% Z / N+ d' n: v/ _# u7 O6 YClass8 W7 l- t8 S6 s/ Z \4 RSec.1.9 Construction of metric outer measure& `( Z0 s3 O/ @
9 J+ j: O/ S9 q' R6 W& G7 J( h
2 D2 b% `" Z4 Q- d1 U& ^- b
Class9 + P$ E6 C( O# g7 E" L6 N( |4 {7 r0 osec.1.10 Signed measure R4 j# H. C/ {( @# w
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4 D8 @3 ? h6 N) x; C" ?Class10& |9 N4 t3 }; h0 l. }" o
' W$ K1 j! n; @9 S# e
6 ^' Z% W5 N, l7 M9 w
Class11 4 @1 e; Z" o4 |3 j& _ }% T第二章 Integration0 t& n& X3 }; B1 @
Sec. 2.2 Operations on measurable functions ( {+ [2 ^- d, \ - R7 ?- z, ` Y. }( ^% y+ Q% x$ _! Y9 h
Class12( n9 a4 O* z9 n
Sec 2.3. Egoroff’s Thm. 1 {4 L8 D9 e7 F& s9 n2 e( g7 z3 G/ F! v; Q8 w( h; I1 M% c3 }3 _
5 g/ t) M9 c' a* O; F m, JClass131 r1 X2 g: Y- D2 @7 @. B
Sec 2.3 Egoroff’s Thm.0 ?$ K' w6 I/ O' U) i. h) D5 S
" J+ }" {# w% W8 n
2 k" r' G/ h( D. yClass14! ^' K b/ d8 u T
Sec 2.4 Convergence in measure 1 [) ]& I* K6 ?) v: p u1 o8 [* `8 V: E& _ d: y, g2 L7 R
" C) ?8 S) S4 t
Class15 - b1 g3 s' O' R3 eSec 2.5 Integrals of simple functions- Z# C2 e0 f2 t& J
' C" E' m7 ?7 }- h5 k: H 6 _6 ~% m; R5 G2 Z$ z6 q$ K4 j7 wClass16 $ J4 O, v9 T3 w {9 H+ E& nSec. 2.6 Integrable functions0 a _0 F# t7 U; k
7 M7 J. l# L: V/ g' C6 b0 m" Q; J
7 ~) H/ a4 |: @6 m$ @
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- m9 w3 s7 t; S( m8 t- M 1 M) O* ~. }' CClass189 [6 B1 \7 A& \" H) k* x3 `* F
Sec. 2.7 Properties of integrals 4 ]6 v! A8 n o0 Q 3 Z" S5 b; L Z [* I, s: T4 H& M. K" X- k) _0 c
Class19-20 * o5 ^) i# j8 L" z. P& I# j& ~* Q0 [" ?2 y9 V( t
3 z! J/ {$ f* lClass21 ' z" X( |) X% [" Y' V! tSec.2.9 DCT ) L, r$ w" Q5 }1 j: f | 1 c" B, z8 C0 k! \4 j: ~+ y9 |3 N/ o7 G: w
Class22 5 f/ W% a; c$ |! d/ p FSec. 2.10 Applications of DCT " x8 H$ U, M$ d0 m9 x: ] B# _- h( [0 f( S+ H & U' ^. D a( T: M5 w* GClass23-24 / u2 P. }8 P, Z: b* ASec 2.11 (Proper) Riemann integral 9 V( |+ z( R( _ Z/ Y1 X8 G3 M7 {0 E
) u2 |' n! d' |Class25* r& [+ E4 }( a/ X
; \. ?+ ]5 W) E* J. Q2 z
0 S8 y8 J% n+ L( X: `# LClass45-46( X6 ^ G4 k& I( |8 n, G8 {: B% X
Sec. 4.4 Linear Transformations$ u3 J7 k3 D7 `# X
9 B' Y/ T# v* @3 V3 n7 V7 `3 A8 O' s {& r: V# J2 D: l
Class47& x" q; l% I8 I& _ p- m
sec. 4.5 Principle of uniform bddness (Banach- Steinhaus Thm)! z3 a, w1 c, a. V5 [
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( a6 e9 s* Q% r3 z' B
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Class50, D6 u2 m- k+ Q8 D
: \; g; T7 o. Q! f9 f% i* k! q- E
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