Theorem 17IFf=0 Q.eHien JAF =o If and only If f=o a.eF Z0proof: (E if F=O ae then SF= F=AIB%3D=の(>) suppose f=0let An = fXcA; rcal> t? Note FZt XamiASoのっAn A8o thn M(An) =0But B= {XEA: Fl2) >0}=204U Ann=13030F= 0QuestionCanAlhe assumphion f Z0be dropped Intheorem 17?.

Given theorem is "If f≥0, then ∫Af=0 if and only if f=0 a.e.". The question is "Can the assumption…

Theorem 17 F zO Hhen sF=0 If and only If f=o Q.e IF SF= fF AIB Proof: (E If F=O Qe then %3D A1B MCB) = 三の (->) suppose S F=0 Tet An= XEA ; F(2) >I Note FZ! AAniA %3D So 0= X. Am iA 8o Hin M(An)= But B= $ }= N An XEA: F(2) >o %3D 30 30 F= 0 Question a Hhe Can the assumption f zo kheorem 17?- be dropped in

Theorem 17 F zO Hhen sF=0 If and only If f=o Q.e IF SF= fF AIB Proof: (E If F=O Qe then %3D A1B MCB) = 三の (->) suppose S F=0 Tet An= XEA ; F(2) >I Note FZ! AAniA %3D So 0= X. Am iA 8o Hin M(An)= But B= $ }= N An XEA: F(2) >o %3D 30 30 F= 0 Question a Hhe Can the assumption f zo kheorem 17?- be dropped in

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 24E: If a0 in a field F, prove that for every bF the equation ax=b has a unique solution x in F. [Type...

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