How do they define luminosity function in astrophysics?

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hi, please explain me how to define a luminosity function? what is meant by luminosity interval? and the last one , what is meant by Present Day Mass Function (PDMF)?

reagrds
 
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The luminosity in astrophysics is usually the total integrated flux of an astrophysical object. In other words, it usually defined as the total radiated power over all wavelengths (energy per unit time, and in SI units measured in Watts, but often measured in Solar luminosities for a star in astrophysical situations) of an astrophysical object. The Sun, for example, has a luminosity of order 4*10^26 Watts.

I have not heard of the terms "luminosity interval" or "PDMF", could you provide some context on where they were used?
 
they are used in compact bodies studies..like white dwarf, neutron star etc