diff --git a/learnware/market/easy/checker.py b/learnware/market/easy/checker.py
index 57cae22..95c0f1a 100644
--- a/learnware/market/easy/checker.py
+++ b/learnware/market/easy/checker.py
@@ -115,7 +115,11 @@ class EasyStatChecker(BaseChecker):
 
             # Check if statistical specification is computable in dist()
             stat_spec = learnware.get_specification().get_stat_spec_by_name(spec_type)
-            stat_spec.dist(stat_spec)
+            distance = float(stat_spec.dist(stat_spec))
+            if not np.isfinite(distance):
+                message = f"The distance between statistical specifications is not finite, where distance={distance}"
+                logger.warning(message)
+                return self.INVALID_LEARNWARE, message
 
             if spec_type == "RKMETableSpecification":
                 if not isinstance(input_shape, tuple) or not all(isinstance(item, int) for item in input_shape):
diff --git a/learnware/market/easy/searcher.py b/learnware/market/easy/searcher.py
index 48bbfa8..7f6690f 100644
--- a/learnware/market/easy/searcher.py
+++ b/learnware/market/easy/searcher.py
@@ -538,14 +538,20 @@ class EasyStatSearcher(BaseSearcher):
             both lists are sorted by mmd dist
         """
         rkme_list = [learnware.specification.get_stat_spec_by_name(self.stat_spec_type) for learnware in learnware_list]
-        mmd_dist_list = []
-        for rkme in rkme_list:
-            mmd_dist = rkme.dist(user_rkme)
-            mmd_dist_list.append(mmd_dist)
+        filtered_idx_list, mmd_dist_list = [], []
+        for idx in range(len(rkme_list)):
+            mmd_dist = float(rkme_list[idx].dist(user_rkme))
+            if np.isfinite(mmd_dist):
+                mmd_dist_list.append(mmd_dist)
+                filtered_idx_list.append(idx)
+            else:
+                logger.warning(
+                    f"The distance between user_spec and learnware_spec (id: {learnware_list[idx].id}) is not finite, where distance is {mmd_dist}"
+                )
 
-        sorted_idx_list = sorted(range(len(learnware_list)), key=lambda k: mmd_dist_list[k])
+        sorted_idx_list = sorted(range(len(mmd_dist_list)), key=lambda k: mmd_dist_list[k])
         sorted_dist_list = [mmd_dist_list[idx] for idx in sorted_idx_list]
-        sorted_learnware_list = [learnware_list[idx] for idx in sorted_idx_list]
+        sorted_learnware_list = [learnware_list[filtered_idx_list[idx]] for idx in sorted_idx_list]
 
         return sorted_dist_list, sorted_learnware_list
 
@@ -561,6 +567,9 @@ class EasyStatSearcher(BaseSearcher):
             raise KeyError("No supported stat specification is given in the user info")
 
         user_rkme = user_info.stat_info[self.stat_spec_type]
+        if not np.isfinite(float(user_rkme.dist(user_rkme))):
+            raise ValueError("The distance between uploaded statistical specifications is not finite!")
+
         learnware_list = self._filter_by_rkme_spec_metadata(learnware_list, user_rkme)
         logger.info(f"After filter by rkme dimension, learnware_list length is {len(learnware_list)}")