Null function and Lebesgue measure on $\mathbb{R}^N$

We know that some measurable function $f:(0,T)\times\Omega\to\mathbb{R}$, where $\Omega\subset\mathbb{R}^N$ has the following property:

For almost all $t\in (0,T)$ (Lebesgue measure in $\mathbb{R}$) we have that:

$f(t,x)=0$for almost all$x\in\Omega$ (Lebesgue measure in$\mathbb{R}^N$).

Is it true that $f(t,x)=0$ for almost all (Lebesgue measure on$(0,T)\times\Omega$)?