theorem Th35: :: MESFUNC9:35

for X being non empty set
for S being SigmaField of X
for F being Functional_Sequence of X,ExtREAL
for n being Nat st ( for m being Nat holds F . m is_simple_func_in S ) holds
( F is additive & (Partial_Sums F) . n is_simple_func_in S )