[1] G. Keller Stochastic stability in some chaotic dynamical systems Monatsh. Math., 94 (4) (1982), pp. 313–333 [2] A. Lasota, J.A. Yorke On the existence of invariant measures for piecewise monotonic transformations Trans. Amer. Math. Soc., 186 (1973), pp. 481–488 MR0335758 (49 #538) (1974) [3] A. Boyarsky, P. Góra Laws of Chaos, Invariant Measures and Dynamical Systems in One Dimension, Probability and its Applications, Birkhaüser, Boston, MA (1997) [4] G. Keller, C. Liverani Stability of the spectrum for transfer operators Ann. Sc. Norm. Super Pisa Cl. Sci. (4), 28 (1) (1999), pp. 141–152 [5] P. Eslami, M. Misiurewicz Singular limits of absolutely continuous invariant measures for families of transitive map J. Difference Equ. Appl., 18 (4) (2012), pp. 739–750 http://dx.doi.org/10.1080/10236198.2011.590480 [6] Zhenyang Li, P. Góra, A. Boyarsky, H. Proppe, P. Eslami, A family of piecewise expanding maps having singular measure as a limit of ACIM’s, Ergodic Theory Dynam. Systems. http://dx.doi.org/10.1017/S0143385711000836 (in press). [7] Zhenyang Li, W-like maps with various instabilities of acim’s. Available at http://arxiv.org/abs/1109.5199. [8] P. Eslami, P. Góra, Stronger Lasota–Yorke inequality for piecewise monotonic transformations. Preprint. [9] P. Collet, J.P. Eckmann Measures invariant under mappings of the unit interval ,in: G. Velo, A.S. Wightman (Eds.), Regular and Chaotic Motions in Dynamic Systems, NATO ASI Series, Series B: Physics, vol. 118, Plenum Press, NY (1985), pp. 233–265 [10] B. Schmitt, Contributions a l’étude de systemes dynamiques unidimensionnels en théorie ergodique, Ph.D. Thesis, University of Bourgogne, 1986. [11] P. Góra Properties of invariant measures for piecewise expanding one-dimensional transformations with summable oscillations of derivative Ergodic Theory Dynam. Systems, 14 (3) (1994), pp. 475–492 [12] M.R. Rychlik, Invariant measures and the variational principle for Lozi mappings, Ph.D. Thesis, University of California, Berkeley, 1983. [13] P. Góra, A. Boyarsky Compactness of invariant densities for families of expanding, piecewise monotonic transformations Canad. J. Math., XLI (1989), pp. 855–869