  The recently published experimental data for specific heat C_p of liquid
helium in zero gravity conditions very close to the lambda-transition have been
discussed. We have shown that these data allow different interpretations. They
can be well interpreted within the perturbative RG approach and within our
recently developed theory, as well. Allowing the logarithmic correction, the
corresponding fits lie almost on top of each other over the whole range of the
reduced temperatures t (for bin averaged data) 6.3 x 10^{-10} < t < 8.8 x
10^{-3}. However, the plot of the effective exponent alpha_eff(t) suggests that
the behaviour of C_p, probably, changes very close to the lambda-transition
temperature. To clarify this question, we need more accurate data for
t<10^{-7}. In addition, we show that the experimental data for superfluid
fraction of liquid helium close to the critical point within 3 x 10^{-7} < t <
10^{-4} can be better fit by our exponents nu=9/13, Delta=5/13 than by the RG
exponents (nu approximately 0.6705 and Delta about 0.5). The latter ones are
preferable to fit the whole measured range 3 x 10^{-7} < t < 10^{-2} where,
however, remarkable systematic deviations appear. Our estimated value 0.694 +/-
0.017 of the asymptotic exponent nu well agrees with the theoretical prediction
nu=9/13.
