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The traditional view that Ly-alpha emission and dust should be mutuallyexclusive has been questioned more and more often; most notably, theobservations of Ly-alpha emission from ULIRGs seem to counter this view. Inthis paper we seek to address the reverse question. How large a fraction ofLy-alpha selected galaxies are ULIRGs? Using two samples of 24/25 Ly-alphaemitting galaxies at z = 0.3/2.3, we perform this test, including results at z= 3.1, and find that, whereas the ULIRG fraction at z = 3.1 is very small, itsystematically increases towards lower redshifts. There is a hint that thisevolution may be quite sudden and that it happens around a redshift of z ~ 2.5.After measuring the infrared luminosities of the Ly-alpha emitters, we findthat they are in the normal to ULIRG range in the lower redshift sample, whilethe higher redshift galaxies all have luminosities in the ULIRG category. TheLy-alpha escape fractions for these infrared bright galaxies are in the range1-100 % in the z = 0.3 galaxies, but are very low in the z = 2.3 galaxies, 0.4% on average. The unobscured star formation rates are very high, ranging from500 to more than 5000 M_sun/yr, and the dust attenuation derived are in therange 0.0 < A_V < 3.5.

Ly-alpha emitters: blue dwarfs or supermassive ULIRGs? Evidence for a transition with redshift