theorem Th28: :: INTEGRA4:28

for a being Real
for A being non empty closed_interval Subset of REAL
for f, g, h being Function of A,REAL st f | A is bounded & f is integrable & g | A is bounded & g is integrable & h | A is bounded & a > 0 & ( for x, y being Real st x in A & y in A holds
|.((h . x) - (h . y)).| <= a * (|.((f . x) - (f . y)).| + |.((g . x) - (g . y)).|) ) holds
h is integrable