theorem Th33: :: MESFUN17:33

for I, J, K being non empty closed_interval Subset of REAL
for f being PartFunc of [:[:RNS_Real,RNS_Real:],RNS_Real:],RNS_Real
for g being PartFunc of [:[:REAL,REAL:],REAL:],REAL
for Fz being PartFunc of [:RNS_Real,RNS_Real:],RNS_Real st [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g & Fz = (Integral2 (L-Meas,|.(R_EAL g).|)) | [:I,J:] holds
Fz is_uniformly_continuous_on [:I,J:]