 In the theory of critical phenomena, free energy of a system near the critical point depends analytically on the coefficients of generic (not dangerous) irrelevant operators, while the dependence on the coefficients of dangeorously irrelevant operators is non-analytic (, p. 49).The presence of dangerously irrelevant operators leads to the violation of the hyperscaling relation formula_1 between the critical exponents formula_2 and formula_3 in formula_4 dimensions.The simplest example (, p. 93) is the critical point of the Ising ferromagnet in formula_5 dimensions, which is a gaussian theory (free massless scalar formula_6), but the leading irrelevant perturbation formula_7 is dangerously irrelevant.