Stars do not form continuously distributed over star forming galaxies. They form in star clusters of different masses. This nature of clustered star formation is taken into account in the theory of the integrated galactic stellar initial mass function (IGIMF) in which the galaxy-wide IMF (the IGIMF) is calculated by adding all IMFs of young star clusters. For massive stars the IGIMF is steeper than the universal IMF in star clusters and steepens with decreasing SFR which is called the IGIMF-effect. The current SFR and the total Halpha luminosity of galaxies therefore scale non-linearly in the IGIMF theory compared to the classical case in which the galaxy-wide IMF is assumed to be constant and identical to the IMF in star clusters. We here apply for the first time the revised SFR-L_Halpha relation on a sample of local volume star forming galaxies with measured Halpha luminosities. The fundamental results are: i) the SFRs of galaxies scale linearly with the total galaxy neutral gas mass, ii) the gas depletion time scales of dwarf irregular and large disk galaxies are about 3 Gyr implying that dwarf galaxies do not have lower star formation efficiencies than large disk galaxies, and iii) the stellar mass buildup times of dwarf and large galaxies are only in agreement with downsizing in the IGIMF context, but contradict downsizing within the traditional framework that assumes a constant galaxy-wide IMF.
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