  We discuss pointwise behavior of weak supersolutions for a class of doubly
nonlinear parabolic fractional $p$-Laplace equations which includes the
fractional parabolic $p$-Laplace equation and the fractional porous medium
equation. More precisely, we show that weak supersolutions have lower
semicontinuous representative. We also prove that the semicontinuous
representative at an instant of time is determined by the values at previous
times. This gives a pointwise interpretation for a weak supersolution at every
point. The corresponding results hold true also for weak subsolutions. Our
results extend some recent results in the local parabolic case and in the
nonlocal elliptic case to the nonlocal parabolic case. We prove the required
energy estimates and measure theoretic De Giorgi type lemmas in the fractional
setting.
