A very good reference for various forms of AC is the book Howard, Rubin: *[Consequences of the Axiom of Choice](https://books.google.com/books?id=ffXxBwAAQBAJ)*. This book contains a large database of various consequence of choice and tables showing relations between them. There is also [a website](http://consequences.emich.edu/conseq.htm) where you can search for relations between various forms mentioned in this book. In this book we can find: > **FORM 142.** $\neg$PB: There is a set of reals without the property of Baire. Jech [1973b] p 7 and note 28. > > **FORM 222.** There is a non-principal measure on $\mathcal P(\omega)$. Pincus/Solovay [1977] and note 147. Then in the table which shows implications between various forms we find: > 222 142 (1) Pincus [1972c]<br> > 142 222 (3) Pincus [1972c] (1) = "The implication is provable."<br> (3) = "The implication is not provable in ZF". The reference given there is: > [1972c] D. Pincus: The strength of the Hahn-Banach theorem, Proc. of the Victoria Symp. on Nonstandard Analysis, Lecture Notes in Math. 369, Springer, Heidelberg, 1973, 203-248. DOI: [10.1007/BFb0066014](http://dx.doi.org/10.1007/BFb0066014). D. Pincus writes there that this implication *"is due to Solovay. It is stated without proof in [20]. Since it may interest readers of this paper we include our own proof at the end of §I."* Where [20] is R. M. Solovay, *A model of set theory in which every set of reals is Lesbague measurable*, Ann. of Math. 92 (1970), pp. 1-58.