return asMap(backingSet().subSet(fromKey, toKey), function);
    }

    @Override
    public SortedMap<K, V> headMap(@ParametricNullness K toKey) {
      return asMap(backingSet().headSet(toKey), function);
    }

    @Override
    public SortedMap<K, V> tailMap(@ParametricNullness K fromKey) {
      return asMap(backingSet().tailSet(fromKey), function);
    }

      return asMap(backingSet().subSet(fromKey, toKey), function);
    }

    @Override
    public SortedMap<K, V> headMap(@ParametricNullness K toKey) {
      return asMap(backingSet().headSet(toKey), function);
    }

    @Override
    public SortedMap<K, V> tailMap(@ParametricNullness K fromKey) {
      return asMap(backingSet().tailSet(fromKey), function);
    }

    // add a non-serializable entry
    one.getUnchecked(new Object());
    assertEquals(1, one.size());
    assertFalse(one.asMap().isEmpty());
    LocalLoadingCache<Object, Object> two = SerializableTester.reserialize(one);
    assertEquals(0, two.size());
    assertTrue(two.asMap().isEmpty());

    LocalCache<Object, Object> localCacheOne = one.localCache;
    LocalCache<Object, Object> localCacheTwo = two.localCache;

    // add a non-serializable entry
    one.getUnchecked(new Object());
    assertEquals(1, one.size());
    assertFalse(one.asMap().isEmpty());
    LocalLoadingCache<Object, Object> two = SerializableTester.reserialize(one);
    assertEquals(0, two.size());
    assertTrue(two.asMap().isEmpty());

    LocalCache<Object, Object> localCacheOne = one.localCache;
    LocalCache<Object, Object> localCacheTwo = two.localCache;

      localCache.clear();
    }

    @Override
    public long size() {
      return localCache.longSize();
    }

    @Override
    public ConcurrentMap<K, V> asMap() {
      return localCache;
    }

    @Override
    public CacheStats stats() {
      SimpleStatsCounter aggregator = new SimpleStatsCounter();