Ibragimov–Iosifescu conjecture for φ-mixing sequences
Ibragimov–Iosifescu conjecture for φ-mixing sequences in probability theory is the collective name for 2 closely related conjectures by Ildar Ibragimov and :ro:Marius Iosifescu. Conjecture 
Let  be a strictly stationary -mixing sequence, for which  and . Then  is asymptotically normally distributed. -mixing coefficients are defined as
,
where  and  are the -algebras generated by the  (respectively ), and -mixing means that . Reformulated:

Suppose  is a strictly stationary sequence of random variables such that
 and  as  (that is, such that it has finite second moments and  as ). Per Ibragimov, under these assumptions, if also  is -mixing, then a central limit theorem holds. Per a closely related conjecture by Iosifescu, under the same hypothesis, a weak invariance principle holds. Both conjectures together formulated in similar terms:

Let  be a strictly stationary, centered, -mixing sequence of random variables such that  and . Then per Ibragimov , and per Iosifescu . Also, a related conjecture by Magda Peligrad states that under the same conditions and with , . Sources 
I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971, p. 393, problem 3. M. Iosifescu, Limit theorems for ϕ-mixing sequences, a survey. In: Proceedings of the Fifth Conference on Probability Theory, Brașov, 1974, pp. 51-57. Publishing House of the Romanian Academy, Bucharest, 1977. Conjectures
Probability theory