Quantum phenomena are discussed using extended measures. The complex m
easurable processes introduced earlier are studied in greater depth in
the context of harmonic oscillators. Some of the fundamental problems
of radiation and interaction of radiation with matter are analysed in
the general frame of extended measure theory. The connection to Feynm
an path integrals is also discussed and it is shown how the present ap
proach circumvents the divergence difficulties particularly in the est
imation of Lamb shift.