(6)若何可积,则f几乎处处有限 证明:令E=EDC 则E323且M+=mEn= lim En 1→0 对每个n,有四mE三(到/(x+ 所以lmmE=0 从而mEmn==m(⌒En)=m( lim e)= lim mE=0 1→0O 1→0(6) 若f可积，则f几乎处处有限. 证明： 令E E n f n = [| | ]  lim 0 n n mE → 所以 = nm E   f x dx   f x dx  + E E n n 对每个 | ( )| | ( )| n，有 ( ) (lim ) lim 0 1 [ | | ] =  = = = → →  = =+ n n n n n n 从而mE f m E m E mE [| | ] 1 , lim f n n n n E E E  =+ = → 则则EE E E 1 1 2 3    =  = E2  E3  且