  To quantify the entanglement is one of the most important topics in quantum
entanglement theory. In [arXiv: 2006.12408], the authors proposed a method to
build a measure from the orginal domain to a larger one. Here we apply that
method to build an entanglement measure from measures for pure states. First,
we present conditions when the entanglement measure is an entanglement monotone
and convex, we also present an interpretation of the smoothed one-shot
entanglement cost under the method here. At last, we present a difference
between the local operation and classical communication (LOCC) and the
separability-preserving (SEPP) operations, then we present the entanglement
measures built from the geometric entanglement measure for pure states by the
convex roof extended method and the method here are equal, at last, we present
the relationship between the concurrence and the entanglement measure built
from concurrence for pure states by the method here on 2 \otimes 2 systems. We
also present the measure is monogamous for 2\otimes 2 \otimes d system.
