:: deftheorem defines is_simple_func_in MESFUN7C:def 13 :
for X being non empty set
for S being SigmaField of X
for f being PartFunc of X,COMPLEX holds
( f is_simple_func_in S iff ex F being Finite_Sep_Sequence of S st
( dom f = union (rng F) & ( for n being Nat
for x, y being Element of X st n in dom F & x in F . n & y in F . n holds
f . x = f . y ) ) );