:: MESFUNC6 semantic presentation
:: deftheorem Def1 defines less_dom MESFUNC6:def 1 :
theorem Th1: :: MESFUNC6:1
theorem Th2: :: MESFUNC6:2
theorem Th3: :: MESFUNC6:3
:: deftheorem Def2 defines less_eq_dom MESFUNC6:def 2 :
theorem Th4: :: MESFUNC6:4
:: deftheorem Def3 defines great_dom MESFUNC6:def 3 :
theorem Th5: :: MESFUNC6:5
:: deftheorem Def4 defines great_eq_dom MESFUNC6:def 4 :
theorem Th6: :: MESFUNC6:6
:: deftheorem Def5 defines eq_dom MESFUNC6:def 5 :
theorem Th7: :: MESFUNC6:7
theorem Th8: :: MESFUNC6:8
theorem Th9: :: MESFUNC6:9
theorem Th10: :: MESFUNC6:10
theorem Th11: :: MESFUNC6:11
:: deftheorem Def6 defines is_measurable_on MESFUNC6:def 6 :
theorem Th12: :: MESFUNC6:12
theorem Th13: :: MESFUNC6:13
theorem Th14: :: MESFUNC6:14
theorem Th15: :: MESFUNC6:15
theorem Th16: :: MESFUNC6:16
theorem Th17: :: MESFUNC6:17
theorem Th18: :: MESFUNC6:18
theorem Th19: :: MESFUNC6:19
theorem Th20: :: MESFUNC6:20
theorem Th21: :: MESFUNC6:21
theorem Th22: :: MESFUNC6:22
theorem Th23: :: MESFUNC6:23
theorem Th24: :: MESFUNC6:24
theorem Th25: :: MESFUNC6:25
theorem Th26: :: MESFUNC6:26
theorem Th27: :: MESFUNC6:27
theorem Th28: :: MESFUNC6:28
theorem Th29: :: MESFUNC6:29
theorem Th30: :: MESFUNC6:30
theorem Th31: :: MESFUNC6:31
theorem Th32: :: MESFUNC6:32
theorem Th33: :: MESFUNC6:33
theorem Th34: :: MESFUNC6:34
theorem Th35: :: MESFUNC6:35
theorem Th36: :: MESFUNC6:36
theorem Th37: :: MESFUNC6:37
theorem Th38: :: MESFUNC6:38
theorem Th39: :: MESFUNC6:39
theorem Th40: :: MESFUNC6:40
theorem Th41: :: MESFUNC6:41
theorem Th42: :: MESFUNC6:42
theorem Th43: :: MESFUNC6:43
theorem Th44: :: MESFUNC6:44
theorem Th45: :: MESFUNC6:45
theorem Th46: :: MESFUNC6:46
theorem Th47: :: MESFUNC6:47
theorem Th48: :: MESFUNC6:48
:: deftheorem Def7 defines is_simple_func_in MESFUNC6:def 7 :
theorem Th49: :: MESFUNC6:49
theorem Th50: :: MESFUNC6:50
theorem Th51: :: MESFUNC6:51
theorem Th52: :: MESFUNC6:52
theorem Th53: :: MESFUNC6:53
theorem Th54: :: MESFUNC6:54
theorem Th55: :: MESFUNC6:55
theorem Th56: :: MESFUNC6:56
theorem Th57: :: MESFUNC6:57
theorem Th58: :: MESFUNC6:58
theorem Th59: :: MESFUNC6:59
theorem Th60: :: MESFUNC6:60
theorem Th61: :: MESFUNC6:61
theorem Th62: :: MESFUNC6:62
theorem Th63: :: MESFUNC6:63
theorem Th64: :: MESFUNC6:64
theorem Th65: :: MESFUNC6:65
theorem Th66: :: MESFUNC6:66
theorem Th67: :: MESFUNC6:67
theorem Th68: :: MESFUNC6:68
theorem Th69: :: MESFUNC6:69
theorem Th70: :: MESFUNC6:70
theorem Th71: :: MESFUNC6:71
Lemma122:
for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X, REAL st f is_simple_func_in S & dom f <> {} & g is_simple_func_in S & dom g = dom f holds
( f + g is_simple_func_in S & dom (f + g) <> {} )
theorem Th72: :: MESFUNC6:72
theorem Th73: :: MESFUNC6:73
theorem Th74: :: MESFUNC6:74
theorem Th75: :: MESFUNC6:75
theorem Th76: :: MESFUNC6:76
theorem Th77: :: MESFUNC6:77
theorem Th78: :: MESFUNC6:78
theorem Th79: :: MESFUNC6:79
theorem Th80: :: MESFUNC6:80
theorem Th81: :: MESFUNC6:81
:: deftheorem Def8 defines Integral MESFUNC6:def 8 :
theorem Th82: :: MESFUNC6:82
theorem Th83: :: MESFUNC6:83
theorem Th84: :: MESFUNC6:84
theorem Th85: :: MESFUNC6:85
theorem Th86: :: MESFUNC6:86
theorem Th87: :: MESFUNC6:87
theorem Th88: :: MESFUNC6:88
theorem Th89: :: MESFUNC6:89
:: deftheorem Def9 defines is_integrable_on MESFUNC6:def 9 :
theorem Th90: :: MESFUNC6:90
theorem Th91: :: MESFUNC6:91
theorem Th92: :: MESFUNC6:92
theorem Th93: :: MESFUNC6:93
theorem Th94: :: MESFUNC6:94
theorem Th95: :: MESFUNC6:95
theorem Th96: :: MESFUNC6:96
theorem Th97: :: MESFUNC6:97
theorem Th98: :: MESFUNC6:98
theorem Th99: :: MESFUNC6:99
theorem Th100: :: MESFUNC6:100
theorem Th101: :: MESFUNC6:101
theorem Th102: :: MESFUNC6:102
:: deftheorem Def10 defines Integral_on MESFUNC6:def 10 :
theorem Th103: :: MESFUNC6:103
theorem Th104: :: MESFUNC6:104