# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## On Ordinary and Standard Lebesgue Measures on $\mathbb{R}^{\infty}$

### Tom 57 / 2009

Bulletin Polish Acad. Sci. Math. 57 (2009), 209-222 MSC: Primary 28Axx, 28Cxx; Secondary 28C20, 28A35. DOI: 10.4064/ba57-3-3

#### Streszczenie

New concepts of Lebesgue measure on $\mathbb{R}^{\infty}$ are proposed and some of their realizations in the $ZFC$ theory are given. Also, it is shown that Baker's both measures [1], [2], Mankiewicz and Preiss–Tišer generators [6] and the measure of [4] are not $\alpha$-standard Lebesgue measures on $\mathbb{R}^{\infty}$ for $\alpha=(1,1,\ldots)$.